subject:(multilevel Krylov multigrid method)

Delft University of Technology

1. Diao, H. (author). Fourier Analysis of Iterative Methods for the Helmholtz Problem.

Degree: 2012, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8

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This thesis attempts to explain the convergence behaviour of solving Helmholtz problem by investigating its spectral properties. Fourier analysis is employ to solve the eigenvalues… (more)

Subjects/Keywords: Helmholtz problem; Krylov subspace methods; multigrid method; multilevel Krylov multigrid method; shifted Laplacian preconditioner; deflation operator; Fourier analysis

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Diao, H. (. (2012). Fourier Analysis of Iterative Methods for the Helmholtz Problem. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8

Chicago Manual of Style (16^th Edition):

Diao, H (author). “Fourier Analysis of Iterative Methods for the Helmholtz Problem.” 2012. Masters Thesis, Delft University of Technology. Accessed April 12, 2021. http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8.

MLA Handbook (7^th Edition):

Diao, H (author). “Fourier Analysis of Iterative Methods for the Helmholtz Problem.” 2012. Web. 12 Apr 2021.

Vancouver:

Diao H(. Fourier Analysis of Iterative Methods for the Helmholtz Problem. [Internet] [Masters thesis]. Delft University of Technology; 2012. [cited 2021 Apr 12]. Available from: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8.

Council of Science Editors:

Diao H(. Fourier Analysis of Iterative Methods for the Helmholtz Problem. [Masters Thesis]. Delft University of Technology; 2012. Available from: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8

Delft University of Technology

2. Sheikh, A.H. Development Of The Helmholtz Solver Based On A Shifted Laplace Preconditioner And A Multigrid Deflation Technique.

Degree: 2014, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; urn:NBN:nl:ui:24-uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; urn:NBN:nl:ui:24-uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; http://resolver.tudelft.nl/uuid:1020f418-b488-4435-81ee-2b4f6a5024e1

► The Helmholtz equation is the simplest possible model for the wave propagation. Perhaps this is the reason, despite denying traditional iterative methods like Krylov sub-space… (more)

▼ The Helmholtz equation is the simplest possible model for the wave propagation. Perhaps this is the reason, despite denying traditional iterative methods like Krylov sub-space methods, Multigrids, etcetera, numerical solution of the Helmholtz equation has been an interesting and abundant problem to researchers since years. The work in this dissertation is also classified as an attempt to develop fast and robust iterative methods for the solution of the Helmholtz equation. This works is specified for applications in seismic imaging-Geophysics, where usually high frequency are used. Thus we will be targeting large wavenumber Helmholtz problems. The finite difference discretization of the Helmholtz equation with typically given Absorbing (Sommerfeld) boundary conditions gives rise to symmetric, non-Hermitian, indefinite linear systems. Resolution of large wavenumber requires larger number of grid points, thus large linear systems. Many (sparse) direct solvers and hybrid (direct and iterative) solvers have been proposed, but it is quite obvious for very large problems that (sparse) direct solvers have been too much depending upon memory, which makes them less acceptable. Quite a lot of work has been invested in researching iterative solution methods for the Helmholtz equation since many decades. The indefiniteness, which increases with respect to an increase in the wavenumber, poses extra problems for iterative solvers and robust solution of indefinite (large) linear system forms an important research activity. Many iterative techniques like domain decomposition methods, multigrid methods and preconditioners for Krylov subspace methods have been proposed but non of them has been quite robust. For multigrid methods, indefiniteness arises difficulties in having both good smoothing property and constructing appropriate coarse-grid approximations of the problem, which are responsible for further reduction of low frequency errors. Many attempts have been spent in algebraic variants of multigrid methods. Some of them works well with limitation of homogeneity. Most of them fails to show satisfactory convergence. The same holds for Krylov subspace methods. One of the difficulties for Krylov methods is to find a cheap and performing preconditioner for the indefinite Helmholtz equation. An overview of preconditioners, ranging from classical to matrix based, for indefinite Helmholtz linear system has been give in this thesis. A matrix-based complex shifted Laplace preconditioner (CSLP) has been seen as best in the available ones. However, with increasing wavenumbers CSLP shows a slow convergence behavior. We address this issue continuing using CSLP while taking care of its requirement of specific complex shifts. The projection-type preconditioners have been widely investigated by researchers in numerical analysis community. We propose the projection-type deflation preconditioner to tackle the near-singular nodes, which are the cause of the decay the convergence of, this otherwise well performing, CSLP. Like multigrid, this… Advisors/Committee Members: Vuik, C..

Subjects/Keywords: Helmholtz; multigrid methods; Krylov; iterative solvers; wave equations; deflation method; multilevel methods

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Sheikh, A. H. (2014). Development Of The Helmholtz Solver Based On A Shifted Laplace Preconditioner And A Multigrid Deflation Technique. (Doctoral Dissertation). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; urn:NBN:nl:ui:24-uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; urn:NBN:nl:ui:24-uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; http://resolver.tudelft.nl/uuid:1020f418-b488-4435-81ee-2b4f6a5024e1

Chicago Manual of Style (16^th Edition):

Sheikh, A H. “Development Of The Helmholtz Solver Based On A Shifted Laplace Preconditioner And A Multigrid Deflation Technique.” 2014. Doctoral Dissertation, Delft University of Technology. Accessed April 12, 2021. http://resolver.tudelft.nl/uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; urn:NBN:nl:ui:24-uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; urn:NBN:nl:ui:24-uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; http://resolver.tudelft.nl/uuid:1020f418-b488-4435-81ee-2b4f6a5024e1.

MLA Handbook (7^th Edition):

Sheikh, A H. “Development Of The Helmholtz Solver Based On A Shifted Laplace Preconditioner And A Multigrid Deflation Technique.” 2014. Web. 12 Apr 2021.

Vancouver:

Sheikh AH. Development Of The Helmholtz Solver Based On A Shifted Laplace Preconditioner And A Multigrid Deflation Technique. [Internet] [Doctoral dissertation]. Delft University of Technology; 2014. [cited 2021 Apr 12]. Available from: http://resolver.tudelft.nl/uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; urn:NBN:nl:ui:24-uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; urn:NBN:nl:ui:24-uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; http://resolver.tudelft.nl/uuid:1020f418-b488-4435-81ee-2b4f6a5024e1.

Council of Science Editors:

Sheikh AH. Development Of The Helmholtz Solver Based On A Shifted Laplace Preconditioner And A Multigrid Deflation Technique. [Doctoral Dissertation]. Delft University of Technology; 2014. Available from: http://resolver.tudelft.nl/uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; urn:NBN:nl:ui:24-uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; urn:NBN:nl:ui:24-uuid:1020f418-b488-4435-81ee-2b4f6a5024e1 ; http://resolver.tudelft.nl/uuid:1020f418-b488-4435-81ee-2b4f6a5024e1

3. Priscila Cardoso Calegari. Simulação computacional de escoamentos reativos com baixo número Mach aplicando técnicas de refinamento adaptativo de malhas.

Degree: 2012, University of São Paulo

URL: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-21082012-051927/

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O foco principal do presente trabalho é estender uma metodologia numérica embasada no uso de uma técnica de refinamento adaptativo de malha (AMR - Adaptive… (more)

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O foco principal do presente trabalho é estender uma metodologia numérica embasada no uso de uma técnica de refinamento adaptativo de malha (AMR - Adaptive Mesh Refinement) e no uso de esquemas temporais multipasso implícitos-explícitos (IMEX) a aplicações envolvendo escoamentos reativos com baixo número de Mach. Originalmente desenvolvida para escoamentos incompressíveis, a formulação euleriana daquela metodologia emprega as equações de Navier-Stokes como modelo matemático para descrever a dinâmica do escoamento e o Método da Projeção, baseado no divergente nulo da velocidade do escoamento, para tratar o acoplamento pressão-velocidade presente na formulação com variáveis primitivas. Tal formulação euleriana original é estendida para acomodar novas equações agregadas ao modelo matemático da fase contínua: conservação de massa, fração de mistura (para representar as concentrações de combustível e oxidante), e energia. Além disso, uma equação termodinâmica de estado é integrada ao modelo matemático estendido e é empregada juntamente com a equação de conservação de massa para produzir uma nova restrição (não nula desta vez) ao divergente do campo de velocidade. Assume-se que o escoamento ocorre a baixo número de Mach (hipótese principal). O Método de Diferença Finita é empregado na discretização espacial das variáveis eulerianas de estado, empregando-se uma malha AMR. As vantagens e dificuldades desta extensão são cuidadosamente investigadas e reportadas. Pela importância, do ponto de vista de aplicações práticas, alguns estudos numéricos preliminares envolvendo escoamentos incompressíveis turbulentos com sprays são realizados (as gotículas compõem a fase dispersa). Num primeiro momento, apenas sprays com gotículas inertes são considerados. Embora ainda apenas iniciais, tais estudos já se mostram importantes pois identificam com clareza, em primeira instância, algumas das dificuldades inerentes a serem enfrentadas ao se tratar dentro desta nova metodologia um conjunto relativamente grande de gotículas lagrangianas. No caso de escoamentos incompressíveis turbulentos com sprays, a integração temporal se dá com métodos IMEX para a fase contínua e com o Método de Euler Modificado para a fase dispersa. A turbulência, em todos os casos que a envolvem, é tratada pelo modelo de Simulação das Grandes Escalas (LES - Large Eddy Simulation). As simulações computacionais se dão em um domínio tridimensional, um parelelepípedo, e empregam uma extensão (resultante do presente trabalho) do código AMR3D, um programa de computador sequencial implementado em Fortran90, oriundo de uma colaboração de longa data entre o IME-USP e o MFLab/FEMEC-UFU (Laboratório de Dinâmica de Fluidos da Universidade Federal de Uberlândia). O processamento foi efetuado no LabMAP (Laboratório da Matemática Aplicada do IME-USP).

It is the main goal of the present work to extend a numerical methodology based on both the use of an adaptive mesh refinement technique (AMR) and the use of a multistep, implicit-explicit time-step strategy (IMEX) to…

Advisors/Committee Members: Alexandre Megiorin Roma, Antonio Castelo Filho, Luis Carlos de Castro Santos, Ricardo Serfaty, Aristeu da Silveira Neto.

Subjects/Keywords: AMR; Baixo Número de Mach; Escoamentos Reativos; IMEX; Método da Projeção; Métodos Multinível-Multigrid; Sprays; AMR; IMEX; Low Mach Number; Multilevel-Multigrid Methods; Projection Method; Reacting Flows; Sprays

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Calegari, P. C. (2012). Simulação computacional de escoamentos reativos com baixo número Mach aplicando técnicas de refinamento adaptativo de malhas. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/45/45132/tde-21082012-051927/

Chicago Manual of Style (16^th Edition):

Calegari, Priscila Cardoso. “Simulação computacional de escoamentos reativos com baixo número Mach aplicando técnicas de refinamento adaptativo de malhas.” 2012. Doctoral Dissertation, University of São Paulo. Accessed April 12, 2021. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-21082012-051927/.

MLA Handbook (7^th Edition):

Calegari, Priscila Cardoso. “Simulação computacional de escoamentos reativos com baixo número Mach aplicando técnicas de refinamento adaptativo de malhas.” 2012. Web. 12 Apr 2021.

Vancouver:

Calegari PC. Simulação computacional de escoamentos reativos com baixo número Mach aplicando técnicas de refinamento adaptativo de malhas. [Internet] [Doctoral dissertation]. University of São Paulo; 2012. [cited 2021 Apr 12]. Available from: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-21082012-051927/.

Council of Science Editors:

Calegari PC. Simulação computacional de escoamentos reativos com baixo número Mach aplicando técnicas de refinamento adaptativo de malhas. [Doctoral Dissertation]. University of São Paulo; 2012. Available from: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-21082012-051927/

4. Wobker, Hilmar. Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems.

Degree: 2010, Technische Universität Dortmund

URL: http://hdl.handle.net/2003/26998

► Bei der Simulation realistischer strukturmechanischer Probleme können Gleichungssysteme mit mehreren hundert Millionen Unbekannten entstehen. Für die effiziente Lösung solcher Systeme sind parallele Multilevel-Methoden unerlässlich, die… (more)

▼ Bei der Simulation realistischer strukturmechanischer Probleme können Gleichungssysteme mit mehreren hundert Millionen Unbekannten entstehen. Für die effiziente Lösung solcher Systeme sind parallele Multilevel-Methoden unerlässlich, die in der Lage sind, die Leistung moderner Hardware-Technologien auszuschöpfen. Die Finite-Elemente- und Löser-Toolbox FEAST, die auf die Behandlung skalarer Gleichungen ausgelegt ist, verfolgt genau dieses Ziel. FEAST kombiniert Hardware-orientierte Implementierungstechniken mit einer Multilevel-Gebietszerlegungsmethode namens ScaRC. In der vorliegenden Arbeit wird ein Konzept entwickelt, multivariate Elastizitätsprobleme basierend auf der FEAST-Bibliothek zu lösen. Die generelle Herangehensweise besteht darin, die Lösung multivariater Probleme auf die Lösung einer Reihe von skalaren Problemen zurückzuführen. Dieser Ansatz ermöglicht eine strikte Trennung von skalaren "low level" Kernfunktionalitäten (in Form der FEAST-Bibliothek) und multivariatem "high level" Anwendungscode (in Form des Elastizitätsproblems), was aus Sicht der Softwareentwicklungstechnik sehr vorteilhaft ist: Alle Bemühungen zur Verbesserung der Hardware-Effizienz, sowie Anpassungen an zukünftige technologische Entwicklungen können auf skalare Operationen beschränkt werden, während die multivariate Anwendung automatisch von diesen Erweiterungen profitiert. Im ersten Teil der Arbeit werden substantielle Verbesserungen der skalaren ScaRC-Löser entwickelt, die dann als essentielle Bausteine zur Lösung multivariater Elastizitätsprobleme eingesetzt werden. Ausführliche numerische Untersuchungen zeigen, wie sich die Effizienz der skalaren FEAST-Bibliothek auf den multivariaten Lösungsprozess überträgt. Die Löserstrategie wird dann auf nichtlineare Probleme der Elastizität mit finiter Deformation angewandt. Durch Einsatz einer Liniensuche-Methode wird die Robustheit des Newton-Raphson-Verfahrens signifikant erhöht. Es werden verschiedene Strategien miteinander verglichen, wie genau die linearen Probleme innerhalb der nichtlinearen Iteration zu lösen sind. Zur Behandlung der wichtigen Klasse von (fast) inkompressiblen Materialien wird eine gemischte Verschiebung/Druck-Formulierung gewählt, die mit Hilfe von stabilisierten bilinearen finiten Elementen (Q1/Q1) diskretisiert wird. Eine erweiterte Version der klassischen "Druck-Poisson"-Stabilisierung wird präsentiert, die auch für hochgradig irreguläre Gitter geeignet ist. Es werden Vor- und Nachteile der Q1/Q1-Diskretisierung erörtert, insbesondere in Bezug auf zeitabhängige Rechnungen. Zwei Löser-Klassen zur Behandlung der entstehenden Sattelpunkt-Probleme werden beschrieben und miteinander verglichen: einerseits verschiedene Arten von (beschleunigten) entkoppelten Lösern (Uzawa, Druck-Schurkomplement-Methoden, Block-Vorkonditionierer), andererseits gekoppelte Mehrgitter-Verfahren mit Vanka-Glättern. Effiziente Schurkomplement-Vorkonditionierer, die für die erste Löser-Klasse notwendig sind, werden im Rahmen statischer und zeitabhängiger Probleme besprochen. Die zentrale… Advisors/Committee Members: Turek, S..

Subjects/Keywords: Adaptive coarse grid correction; Adaptive Grobgitterkorrektur; Damped Newton-Raphson; Domain decomposition; Elasticity; Elastizität; Elastodynamic; Elastodynamisch; Elastostatic; Elastostatisch; Equal-order finite elements; FEAST; FEAST; Festkörpermechanik; Finite deformation; Finite Deformation; Finite-Elemente-Methode; Finite element method; Gebietszerlegung; Gedämpftes Newton-Raphson; Gemischte Formulierung; Globales Newton-Raphson; Global Newton-Raphson; Große Deformation; Großskalig; Hardware-oriented; Hardware-orientiert; High performance computing; Incompressible material; Inexact Newton-Raphson; Inexaktes Newton-Raphson; Inkompressibles Material; Irreguläres Gitter; Irregular grids; Iterativer Löser; Iterative solver; Large deformation; Large-scale; LBB stabilisation; LBB Stabilisierung; Line-search; Liniensuche; Mehrgitter; Mehrgitter-Krylov; Minimale Überlappung; Minimal overlap; Mixed formulation; Multigrid; Multigrid-Krylov; Multilevel; Multilevel; Newton-Raphson; Nicht-konformes Mehrgitter; Nonconforming multigrid; Parallel computing; Parallele Effizienz; Parallel efficiency; Paralleles Rechnen; Saddle point problem; Sattelpunkt-Problem; ScaRC; ScaRC; Schubversteifung; Schur complement preconditioning; Schurkomplement-Vorkonditionierer; Shear locking; Solid mechanics; Structural mechanics; Strukturmechanik; Transient; Vanka; Vanka; Volume locking; Volumenversteifung; Zeitabhängig; 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Wobker, H. (2010). Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems. (Thesis). Technische Universität Dortmund. Retrieved from http://hdl.handle.net/2003/26998

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Wobker, Hilmar. “Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems.” 2010. Thesis, Technische Universität Dortmund. Accessed April 12, 2021. http://hdl.handle.net/2003/26998.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Wobker, Hilmar. “Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems.” 2010. Web. 12 Apr 2021.

Vancouver:

Wobker H. Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems. [Internet] [Thesis]. Technische Universität Dortmund; 2010. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/2003/26998.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Wobker H. Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems. [Thesis]. Technische Universität Dortmund; 2010. Available from: http://hdl.handle.net/2003/26998

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Colorado

5. Kong, Fande. A Parallel Implicit Fluid-structure Interaction Solver with Isogeometric Coarse Spaces for 3D Unstructured Mesh Problems with Complex Geometry.

Degree: PhD, Computer Science, 2016, University of Colorado

URL: https://scholar.colorado.edu/csci_gradetds/119

► High-resolution simulation of fluid-structure interaction (FSI) problems on supercomputers has many applications including our targeting application in hemodynamics, but most existing methods and software… (more)

▼ High-resolution simulation of fluid-structure interaction (FSI) problems on supercomputers has many applications including our targeting application in hemodynamics, but most existing methods and software do not scale to a large number of processor cores (more than O(10⁴)) when the computational domain is complex and highly unstructured meshes have to be employed. In this thesis, we develop a highly scalable parallel nonlinear solver for fluid-structure interaction problems on unstructured meshes with complex geometry in 3D. The proposed approach consists of several ingredients: a monolithic coupling technique for the fluid and the solid equations, a fully implicit nonlinear solver, and a highly scalable multilevel overlapping Schwarz preconditioner based on isogeometric coarse spaces. In the monolithic coupling approach, the incompressible Navier-Stokes equations for the fluid is formulated in an arbitrary Lagrangian-Euler framework in which an additional partial differential equation is used to describe the motion of the fluid domain. For the solid, a linear or nonlinear elasticity equation is described in the Lagrangian configuration, and the coupling conditions between the fluid and the solid are implicitly enforced on the wet interface. The fluid system is discretized by a finite element method together with SUPG stabilization, and the fluid domain motion and the solid equations are discretized by a finite element method. The semi-discretized system is further discretized in time by implicit schemes such as the backward Euler and the second-order backward difference formula. The coupled FSI system of equations is highly nonlinear and consists of hyperbolic, elliptic, parabolic components in a single system. We develop an inexact Newton-Krylov-Schwarz (NKS) method for solving the coupled FSI system of equations. The focus is on the scalability and the robustness of the algorithms with respect to different physics parameters on 3D unstructured meshes with complex geometry and on supercomputers with a large number of processor cores. The parallel scalability of the NKS method depends almost completely on how the Jacobian system is solved and how a preconditioner is constructed. The main contribution of the thesis is a scalable preconditioner based on new non-standard coarse spaces. The new approach is developed based on the observation that the geometry of the fine mesh, including the fluid mesh and the solid mesh, is vital for the fast convergence of the linear solver. Therefore, a geometry preserving coarsening algorithm is introduced to generate isogeometric coarse meshes that share the same geometry as the fine mesh. The basic idea of the new coarsening algorithm is to retain all the vertices on the boundaries and the wet interface for preserving the geometry of the fine mesh and to coarsen the interior of the fine mesh as much as possible for saving the compute time on coarse levels. The quality of isogeometric coarse meshes is bad in the traditional sense but it is… Advisors/Committee Members: Xiao-Chuan Cai, Jed Brown, Elizabeth R. Jessup, Vitaly Kheyfets, Congming Li.

Subjects/Keywords: Finite element method; Fluid-structure interaction; Mesh coarsening algorithm; Multilevel Schwarz preconditioner; Newton-Krylov-Schwarz; Parallel software development; Numerical Analysis and Scientific Computing; Partial Differential Equations

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Kong, F. (2016). A Parallel Implicit Fluid-structure Interaction Solver with Isogeometric Coarse Spaces for 3D Unstructured Mesh Problems with Complex Geometry. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/csci_gradetds/119

Chicago Manual of Style (16^th Edition):

Kong, Fande. “A Parallel Implicit Fluid-structure Interaction Solver with Isogeometric Coarse Spaces for 3D Unstructured Mesh Problems with Complex Geometry.” 2016. Doctoral Dissertation, University of Colorado. Accessed April 12, 2021. https://scholar.colorado.edu/csci_gradetds/119.

MLA Handbook (7^th Edition):

Kong, Fande. “A Parallel Implicit Fluid-structure Interaction Solver with Isogeometric Coarse Spaces for 3D Unstructured Mesh Problems with Complex Geometry.” 2016. Web. 12 Apr 2021.

Vancouver:

Kong F. A Parallel Implicit Fluid-structure Interaction Solver with Isogeometric Coarse Spaces for 3D Unstructured Mesh Problems with Complex Geometry. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Apr 12]. Available from: https://scholar.colorado.edu/csci_gradetds/119.

Council of Science Editors:

Kong F. A Parallel Implicit Fluid-structure Interaction Solver with Isogeometric Coarse Spaces for 3D Unstructured Mesh Problems with Complex Geometry. [Doctoral Dissertation]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/csci_gradetds/119

6. Duminil, Sébastien. Extrapolation vectorielle et applications aux équations aux dérivées partielles : Vector extrapolation and applications to partial differential equations.

Degree: Docteur es, Mathématiques appliquées, 2012, Littoral

URL: http://www.theses.fr/2012DUNK0336

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Nous nous intéressons, dans cette thèse, à l'étude des méthodes d'extrapolation polynômiales et à l'application de ces méthodes dans l'accélération de méthodes de points fixes… (more)

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Nous nous intéressons, dans cette thèse, à l'étude des méthodes d'extrapolation polynômiales et à l'application de ces méthodes dans l'accélération de méthodes de points fixes pour des problèmes donnés. L'avantage de ces méthodes d'extrapolation est qu'elles utilisent uniquement une suite de vecteurs qui n'est pas forcément convergente, ou qui converge très lentement pour créer une nouvelle suite pouvant admettreune convergence quadratique. Le développement de méthodes cycliques permet, deplus, de limiter le coût de calculs et de stockage. Nous appliquons ces méthodes à la résolution des équations de Navier-Stokes stationnaires et incompressibles, à la résolution de la formulation Kohn-Sham de l'équation de Schrödinger et à la résolution d'équations elliptiques utilisant des méthodes multigrilles. Dans tous les cas, l'efficacité des méthodes d'extrapolation a été montrée.Nous montrons que lorsqu'elles sont appliquées à la résolution de systèmes linéaires, les méthodes d'extrapolation sont comparables aux méthodes de sous espaces de Krylov. En particulier, nous montrons l'équivalence entre la méthode MMPE et CMRH. Nous nous intéressons enfin, à la parallélisation de la méthode CMRH sur des processeurs à mémoire distribuée et à la recherche de préconditionneurs efficaces pour cette même méthode.

In this thesis, we study polynomial extrapolation methods. We discuss the design and implementation of these methods for computing solutions of fixed point methods. Extrapolation methods transform the original sequance into another sequence that converges to the same limit faster than the original one without having explicit knowledge of the sequence generator. Restarted methods permit to keep the storage requirement and the average of computational cost low. We apply these methods for computing steady state solutions of incompressible flow problems modelled by the Navier-Stokes equations, for solving the Schrödinger equation using the Kohn-Sham formulation and for solving elliptic equations using multigrid methods. In all cases, vector extrapolation methods have a useful role to play. We show that, when applied to linearly generated vector sequences, extrapolation methods are related to Krylov subspace methods. For example, we show that the MMPE approach is mathematically equivalent to CMRH method. We present an implementation of the CMRH iterative method suitable for parallel architectures with distributed memory. Finally, we present a preconditioned CMRH method.

Advisors/Committee Members: Sadok, Hassane (thesis director).

Subjects/Keywords: Extrapolation vectorielle; RRE; MPE; MMPE; Systèmes linéaires; Méthodes de Krylov; CMRH; Implémentation parallèle; CMRH préconditionnée; Systèmes non linéaires; Équations de Navier-Stokes; Équations de Schrödinger; Méthodes multigrilles; Vector extrapolation; Reduced Rank Extrapolation; Minimal Polynomial Extrapolation; Modified Minimal Polynomial Extrapolation; Linear systems; Krylov method; CMRH; Parallel implementation; Preconditioned CMRH; Nonlinear systems; Navier-Stokes problem; Schrödinger equation; Multigrid method

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Duminil, S. (2012). Extrapolation vectorielle et applications aux équations aux dérivées partielles : Vector extrapolation and applications to partial differential equations. (Doctoral Dissertation). Littoral. Retrieved from http://www.theses.fr/2012DUNK0336

Chicago Manual of Style (16^th Edition):

Duminil, Sébastien. “Extrapolation vectorielle et applications aux équations aux dérivées partielles : Vector extrapolation and applications to partial differential equations.” 2012. Doctoral Dissertation, Littoral. Accessed April 12, 2021. http://www.theses.fr/2012DUNK0336.

MLA Handbook (7^th Edition):

Duminil, Sébastien. “Extrapolation vectorielle et applications aux équations aux dérivées partielles : Vector extrapolation and applications to partial differential equations.” 2012. Web. 12 Apr 2021.

Vancouver:

Duminil S. Extrapolation vectorielle et applications aux équations aux dérivées partielles : Vector extrapolation and applications to partial differential equations. [Internet] [Doctoral dissertation]. Littoral; 2012. [cited 2021 Apr 12]. Available from: http://www.theses.fr/2012DUNK0336.

Council of Science Editors:

Duminil S. Extrapolation vectorielle et applications aux équations aux dérivées partielles : Vector extrapolation and applications to partial differential equations. [Doctoral Dissertation]. Littoral; 2012. Available from: http://www.theses.fr/2012DUNK0336

7. Liu, Jun. NEW COMPUTATIONAL METHODS FOR OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS.

Degree: PhD, Mathematics, 2015, Southern Illinois University

URL: https://opensiuc.lib.siu.edu/dissertations/1076

► Partial differential equations are the chief means of providing mathematical models in science, engineering and other fields. Optimal control of partial differential equations (PDEs)… (more)

▼ Partial differential equations are the chief means of providing mathematical models in science, engineering and other fields. Optimal control of partial differential equations (PDEs) has tremendous applications in engineering and science, such as shape optimization, image processing, fluid dynamics, and chemical processes. In this thesis, we develop and analyze several efficient numerical methods for the optimal control problems governed by elliptic PDE, parabolic PDE, and wave PDE, respectively. The thesis consists of six chapters. In Chapter 1, we briefly introduce a few motivating applications and summarize some theoretical and computational foundations of our following developed approaches. In Chapter 2, we establish a new multigrid algorithm to accelerate the semi-smooth Newton method that is applied to the first-order necessary optimality system arising from semi-linear control-constrained elliptic optimal control problems. Under suitable assumptions, the discretized Jacobian matrix is proved to have a uniformly bounded inverse with respect to mesh size. Different from current available approaches, a new strategy that leads to a robust multigrid solver is employed to define the coarse grid operator. Numerical simulations are provided to illustrate the efficiency of the proposed method, which shows to be computationally more efficient than the popular full approximation storage (FAS) multigrid method. In particular, our proposed approach achieves a mesh-independent convergence and its performance is highly robust with respect to the regularization parameter. In Chaper 3, we present a new second-order leapfrog finite difference scheme in time for solving the first-order necessary optimality system of the linear parabolic optimal control problems. The new leapfrog scheme is shown to be unconditionally stable and it provides a second-order accuracy, while the classical leapfrog scheme usually is well-known to be unstable. A mathematical proof for the convergence of the proposed scheme is provided under a suitable norm. Moreover, the proposed leapfrog scheme gives a favorable structure that leads to an effective implementation of a fast solver under the multigrid framework. Numerical examples show that the proposed scheme significantly outperforms the widely used second-order backward time differentiation approach, and the resultant fast solver demonstrates a mesh-independent convergence as well as a linear time complexity. In Chapter 4, we develop a new semi-smooth Newton multigrid algorithm for solving the discretized first-order necessary optimality system that characterizes the optimal solution of semi-linear parabolic PDE optimal control problems with control constraints. A new leapfrog discretization scheme in time associated with the standard five-point stencil in space is established to achieve a second-order accuracy. The convergence (or unconditional stability) of the proposed scheme is proved when time-periodic solutions are considered. Moreover, the derived well-structured discretized Jacobian… Advisors/Committee Members: Xiao, Mingqing.

Subjects/Keywords: finite difference scheme; multigrid method; optimal control; partial differential equations; preconditioned Krylov subspace method; semi-smooth Newton method

…102.14 1.4.2 Krylov subspace method In the case of hyperbolic PDEs, multigrid methods turn… …16 1.4.1 Multigrid method… …16 1.4.2 Krylov subspace method… …23 1.5.2 Full approximation scheme (FAS) multigrid method… …25 A new SSN-multigrid method for semilinear elliptic control problems with control…

11 more images…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Liu, J. (2015). NEW COMPUTATIONAL METHODS FOR OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS. (Doctoral Dissertation). Southern Illinois University. Retrieved from https://opensiuc.lib.siu.edu/dissertations/1076

Chicago Manual of Style (16^th Edition):

Liu, Jun. “NEW COMPUTATIONAL METHODS FOR OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS.” 2015. Doctoral Dissertation, Southern Illinois University. Accessed April 12, 2021. https://opensiuc.lib.siu.edu/dissertations/1076.

MLA Handbook (7^th Edition):

Liu, Jun. “NEW COMPUTATIONAL METHODS FOR OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS.” 2015. Web. 12 Apr 2021.

Vancouver:

Liu J. NEW COMPUTATIONAL METHODS FOR OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS. [Internet] [Doctoral dissertation]. Southern Illinois University; 2015. [cited 2021 Apr 12]. Available from: https://opensiuc.lib.siu.edu/dissertations/1076.

Council of Science Editors:

Liu J. NEW COMPUTATIONAL METHODS FOR OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS. [Doctoral Dissertation]. Southern Illinois University; 2015. Available from: https://opensiuc.lib.siu.edu/dissertations/1076

8. Wobker, Hilmar. Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems.

Degree: 2010, Technische Universität Dortmund

URL: http://dx.doi.org/10.17877/DE290R-497

► In the simulation of realistic solid mechanical problems, linear equation systems with hundreds of million unknowns can arise. For the efficient solution of such systems,… (more)

▼ In the simulation of realistic solid mechanical problems, linear equation systems with hundreds of million unknowns can arise. For the efficient solution of such systems, parallel multilevel methods are mandatory that are able to exploit the capabilities of modern hardware technologies. The finite element and solution toolbox FEAST, which is designed to solve scalar equations, pursues exactly this goal. It combines hardware-oriented implementation techniques with a multilevel domain decomposition method called ScaRC that achieves high numerical and parallel efficiency. In this thesis a concept is developed to solve multivariate elasticity problems based on the FEAST library. The general strategy is to reduce the solution of multivariate problems to the solution of a series of scalar problems. This approach facilitates a strict separation of 'low level' scalar kernel functionalities (in the form of the FEAST library) and 'high level' multivariate application code (in the form of the elasticity problem), which is very attractive from a software-engineering point of view: All efforts to improve hardware-efficiency and adaptations to future technology trends can be restricted to scalar operations, and the multivariate application automatically benefits from these enhancements. In the first part of the thesis, substantial improvements of the scalar ScaRC solvers are developed, which are then used as essential building blocks for the efficient solution of multivariate elasticity problems. Extensive numerical studies demonstrate how the efficiency of the scalar FEAST library transfers to the multivariate solution process. The solver strategy is then applied to treat nonlinear problems of finite deformation elasticity. A line-search method is used to significantly increase the robustness of the Newton-Raphson method, and different strategies are compared how to choose the accuracy of the linear system solves within the nonlinear iteration. In order to treat the important class of (nearly) incompressible material, a mixed displacement/pressure formulation is used which is discretised with stabilised bilinear finite elements (Q1/Q1). An enhanced version of the classical 'pressure Poisson' stabilisation is presented which is suitable for highly irregular meshes. Advantages and disadvantages of the Q1/Q1 discretisation are discussed, especially in the context of transient computations. Two solver classes for the resulting saddle point systems are described and compared: on the one hand various kinds of (accelerated) segregated solvers (Uzawa, pressure Schur complement methods, block preconditioners), and on the other hand coupled multigrid solvers with Vanka-smoothers. Efficient Schur complement preconditioners, which are required for the former class, are discussed for the static and the transient case. The main strategy to reduce the solution of multivariate systems to the solution of scalar systems is only applicable in the case of segregated methods. It is shown that for the class of elasticity problems considered in this… Advisors/Committee Members: Turek, S. (advisor), Suttmeier, F.-T. (referee).

Subjects/Keywords: Iterativer Löser; Multilevel; Mehrgitter; Gebietszerlegung; Mehrgitter-Krylov; Nicht-konformes Mehrgitter; ScaRC; Adaptive Grobgitterkorrektur; Minimale Überlappung; Sattelpunkt-Problem; Schurkomplement-Vorkonditionierer; Vanka; Gedämpftes Newton-Raphson; Globales Newton-Raphson; Inexaktes Newton-Raphson; Liniensuche; FEAST; Hardware-orientiert; Großskalig; Paralleles Rechnen; Parallele Effizienz; Finite-Elemente-Methode; Gemischte Formulierung; LBB Stabilisierung; Irreguläres Gitter; Festkörpermechanik; Strukturmechanik; Elastizität; Elastostatisch; Elastodynamisch; Zeitabhängig; Inkompressibles Material; Finite Deformation; Große Deformation; Volumenversteifung; Schubversteifung; Iterative solver; Multilevel; Multigrid; Domain decomposition; Multigrid-Krylov; Nonconforming multigrid; ScaRC; Adaptive coarse grid correction; Minimal overlap; Saddle point problem; Schur complement preconditioning; Vanka; Newton-Raphson; Damped Newton-Raphson; Global Newton-Raphson; Inexact Newton-Raphson; Line-search; FEAST; High performance computing; Hardware-oriented; Large-scale; Parallel computing; Parallel efficiency; Finite element method; Mixed formulation; LBB stabilisation; Equal-order finite elements; Irregular grids; Solid mechanics; Structural mechanics; Elasticity; Elastostatic; Elastodynamic; Transient; Incompressible material; Finite deformation; Large deformation; Volume locking; Shear locking; 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Wobker, H. (2010). Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems. (Doctoral Dissertation). Technische Universität Dortmund. Retrieved from http://dx.doi.org/10.17877/DE290R-497

Chicago Manual of Style (16^th Edition):

Wobker, Hilmar. “Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems.” 2010. Doctoral Dissertation, Technische Universität Dortmund. Accessed April 12, 2021. http://dx.doi.org/10.17877/DE290R-497.

MLA Handbook (7^th Edition):

Wobker, Hilmar. “Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems.” 2010. Web. 12 Apr 2021.

Vancouver:

Wobker H. Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems. [Internet] [Doctoral dissertation]. Technische Universität Dortmund; 2010. [cited 2021 Apr 12]. Available from: http://dx.doi.org/10.17877/DE290R-497.

Council of Science Editors:

Wobker H. Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems. [Doctoral Dissertation]. Technische Universität Dortmund; 2010. Available from: http://dx.doi.org/10.17877/DE290R-497

University of Texas – Austin

9. -5494-1880. Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics.

Degree: PhD, Aerospace Engineering, 2019, University of Texas – Austin

URL: http://dx.doi.org/10.26153/tsw/5474

► The hybridized discontinuous Galerkin methods (HDG) introduced a decade ago is a promising candidate for high-order spatial discretization combined with implicit/implicit-explicit time stepping. Roughly speaking,… (more)

▼ The hybridized discontinuous Galerkin methods (HDG) introduced a decade ago is a promising candidate for high-order spatial discretization combined with implicit/implicit-explicit time stepping. Roughly speaking, HDG methods combines the advantages of both discontinuous Galerkin (DG) methods and hybridized methods. In particular, it enjoys the benefits of equal order spaces, upwinding and ability to handle large gradients of DG methods as well as the smaller globally coupled linear system, adaptivity, and multinumeric capabilities of hybridized methods. However, the main bottleneck in HDG methods, limiting its use to small to moderate sized problems, is the lack of scalable linear solvers. In this thesis we develop fast and scalable solvers for HDG methods consisting of domain decomposition, multigrid and multilevel solvers/preconditioners with an ultimate focus on simulating large scale problems in fluid dynamics and magnetohydrodynamics (MHD). First, we propose a domain decomposition based solver namely iterative HDG for partial differential equations (PDEs). It is a fixed point iterative scheme, with each iteration consisting only of element-by-element and face-by-face embarrassingly parallel solves. Using energy analysis we prove the convergence of the schemes for scalar and system of hyperbolic PDEs and verify the results numerically. We then propose a novel geometric multigrid approach for HDG methods based on fine scale Dirichlet-to-Neumann maps. The algorithm combines the robustness of algebraic multigrid methods due to operator dependent intergrid transfer operators and at the same time has fixed coarse grid construction costs due to its geometric nature. For diffusion dominated PDEs such as the Poisson and the Stokes equations the algorithm gives almost perfect hp – scalability. Next, we propose a multilevel algorithm by combining the concepts of nested dissection, a fill-in reducing ordering strategy, variational structure and high-order properties of HDG, and domain decomposition. Thanks to its root in direct solver strategy the performance of the solver is almost independent of the nature of the PDEs and mostly depends on the smoothness of the solution. We demonstrate this numerically with several prototypical PDEs. Finally, we propose a block preconditioning strategy for HDG applied to incompressible visco-resistive MHD. We use a least squares commutator approximation for the inverse of the Schur complement and algebraic multigrid or the multilevel preconditioner for the approximate inverse of the nodal block. With several 2D and 3D transient examples we demonstrate the robustness and parallel scalability of the block preconditioner Advisors/Committee Members: Bui-Thanh, Tan (advisor), Demkowicz, Leszek F (committee member), Ghattas, Omar (committee member), Raja, Laxminarayan L (committee member), Shadid, John N (committee member), Waelbroeck, Francois L (committee member), Wheeler, Mary F (committee member).

Subjects/Keywords: Hybridized discontinuous Galerkin; Fast solvers; Multigrid; Multilevel; MHD; Domain decomposition

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

-5494-1880. (2019). Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/5474

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-5494-1880. “Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics.” 2019. Doctoral Dissertation, University of Texas – Austin. Accessed April 12, 2021. http://dx.doi.org/10.26153/tsw/5474.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-5494-1880. “Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics.” 2019. Web. 12 Apr 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-5494-1880. Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2019. [cited 2021 Apr 12]. Available from: http://dx.doi.org/10.26153/tsw/5474.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-5494-1880. Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics. [Doctoral Dissertation]. University of Texas – Austin; 2019. Available from: http://dx.doi.org/10.26153/tsw/5474

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

INP Toulouse

10. Pinel, Xavier. A perturbed two-level preconditioner for the solution of three-dimensional heterogeneous Helmholtz problems with applications to geophysics : Un preconditionnement perturbé à deux niveaux pour la résolution de problèmes d'Helmholtz hétérogènes dans le cadre d'une application en géophysique.

Degree: Docteur es, Mathématiques, Informatiques et Télécommunication, 2010, INP Toulouse

URL: http://www.theses.fr/2010INPT0033

►

Le sujet de cette thèse est le développement de méthodes itératives permettant la résolution degrands systèmes linéaires creux d'équations présentant plusieurs seconds membres simultanément. Ces… (more)

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Le sujet de cette thèse est le développement de méthodes itératives permettant la résolution degrands systèmes linéaires creux d'équations présentant plusieurs seconds membres simultanément. Ces méthodes seront en particulier utilisées dans le cadre d'une application géophysique : la migration sismique visant à simuler la propagation d'ondes sous la surface de la terre. Le problème prend la forme d'une équation d'Helmholtz dans le domaine fréquentiel en trois dimensions, discrétisée par des différences finies et donnant lieu à un système linéaire creux, complexe, non-symétrique, non-hermitien. De plus, lorsque de grands nombres d'onde sont considérés, cette matrice possède une taille élevée et est indéfinie. Du fait de ces propriétés, nous nous proposons d'étudier des méthodes de Krylov préconditionnées par des techniques hiérarchiques deux niveaux. Un tel pre-conditionnement s'est montré particulièrement efficace en deux dimensions et le but de cette thèse est de relever le défi de l'adapter au cas tridimensionel. Pour ce faire, des méthodes de Krylov sont utilisées à la fois comme lisseur et comme méthode de résolution du problème grossier. Ces derniers choix induisent l'emploi de méthodes de Krylov dites flexibles.

The topic of this PhD thesis is the development of iterative methods for the solution of large sparse linear systems of equations with possibly multiple right-hand sides given at once. These methods will be used for a specific application in geophysics - seismic migration - related to the simulation of wave propagation in the subsurface of the Earth. Here the three-dimensional Helmholtz equation written in the frequency domain is considered. The finite difference discretization of the Helmholtz equation with the Perfect Matched Layer formulation produces, when high frequencies are considered, a complex linear system which is large, non-symmetric, non-Hermitian, indefinite and sparse. Thus we propose to study preconditioned flexible Krylov subspace methods, especially minimum residual norm methods, to solve this class of problems. As a preconditioner we consider multi-level techniques and especially focus on a two-level method. This twolevel preconditioner has shown efficient for two-dimensional applications and the purpose of this thesis is to extend this to the challenging three-dimensional case. This leads us to propose and analyze a perturbed two-level preconditioner for a flexible Krylov subspace method, where Krylov methods are used both as smoother and as approximate coarse grid solver.

Advisors/Committee Members: Gratton, Serge (thesis director).

Subjects/Keywords: Equation d'Helmholtz; Méthodes de Krylov; Multigrille; Analyse de Fourier; Programmation parrallèle; Seconds membres multiples; Krylov methods; Multigrid; Helmholtz problems; Fourier analysis; Super computers; Geophysics; Multiple right-hand sides problems

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Pinel, X. (2010). A perturbed two-level preconditioner for the solution of three-dimensional heterogeneous Helmholtz problems with applications to geophysics : Un preconditionnement perturbé à deux niveaux pour la résolution de problèmes d'Helmholtz hétérogènes dans le cadre d'une application en géophysique. (Doctoral Dissertation). INP Toulouse. Retrieved from http://www.theses.fr/2010INPT0033

Chicago Manual of Style (16^th Edition):

Pinel, Xavier. “A perturbed two-level preconditioner for the solution of three-dimensional heterogeneous Helmholtz problems with applications to geophysics : Un preconditionnement perturbé à deux niveaux pour la résolution de problèmes d'Helmholtz hétérogènes dans le cadre d'une application en géophysique.” 2010. Doctoral Dissertation, INP Toulouse. Accessed April 12, 2021. http://www.theses.fr/2010INPT0033.

MLA Handbook (7^th Edition):

Pinel, Xavier. “A perturbed two-level preconditioner for the solution of three-dimensional heterogeneous Helmholtz problems with applications to geophysics : Un preconditionnement perturbé à deux niveaux pour la résolution de problèmes d'Helmholtz hétérogènes dans le cadre d'une application en géophysique.” 2010. Web. 12 Apr 2021.

Vancouver:

Pinel X. A perturbed two-level preconditioner for the solution of three-dimensional heterogeneous Helmholtz problems with applications to geophysics : Un preconditionnement perturbé à deux niveaux pour la résolution de problèmes d'Helmholtz hétérogènes dans le cadre d'une application en géophysique. [Internet] [Doctoral dissertation]. INP Toulouse; 2010. [cited 2021 Apr 12]. Available from: http://www.theses.fr/2010INPT0033.

Council of Science Editors:

Pinel X. A perturbed two-level preconditioner for the solution of three-dimensional heterogeneous Helmholtz problems with applications to geophysics : Un preconditionnement perturbé à deux niveaux pour la résolution de problèmes d'Helmholtz hétérogènes dans le cadre d'une application en géophysique. [Doctoral Dissertation]. INP Toulouse; 2010. Available from: http://www.theses.fr/2010INPT0033

11. Millena Martins Villar. Detailed Two-Dimensional Numerical Analysis of Multiphase Flows.

Degree: 2007, Federal University of Uberlândia

URL: http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825

►

The mathematical modeling of multiphase ows involves the interaction between deformable and moving geometries with the uid in which they are dispersed (immersed). This kind… (more)

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The mathematical modeling of multiphase ows involves the interaction between deformable and moving geometries with the uid in which they are dispersed (immersed). This kind of interaction is present in many practical applications. A common approach to handle these problems is the so called Front-Tracking/Front-Capturing Hybrid Methods. This methodology consists in separating the problem into two domains: an eulerian domain, which is kept xed and is used to discretize the uid equations of both phases, and a lagrangian domain, which is used to solve the equations of motion of the interface. Since there is no geometric dependence between these two domains, the method can easily handle moving and deformable interfaces that are dispersed in the ow. Following this line of research, the present work aims to capture accurately details of such ows by resolving adequately the relevant physical scales in time and in space. This can be achieved by applying locally rened meshes which adapt dynamically to cover special ow regions, e.g. the vicinity of the uid-uid interfaces. To obtain the required resolution in time, a semi-implicit second order discretization to solve the Navier-Stokes equations is used. The turbulence modeling is introduced in the present work through Large Eddy Simulation. The eciency and robustness of the methodology applied are veried via convergence analysis, as well as with simulations of one-phase and two-phase ows for several Reynolds numbers. The results of two-phase ows, with one bubble and with multiple bubbles, are presented. The results obtained for a single bubble case are compared with Clift s shape diagram (Clift et al., 1978).

A modelagem matemÃtica de escoamentos multifÃsicos envolve a interaÃÃo de geometrias mÃveis e deformÃveis com o meio fluido que as envolve. Este tipo de interaÃÃo faz parte de uma extensa lista de aplicaÃÃes. Uma linha proposta para o tratamento num Ãrico deste tipo de problema sÃo os mÃtodos hÃbridos Front-Tracking/Front-Capturing. Esta abordagem leva Ã separaÃÃo do problema em dois domÃnios distintos (lÃquido/gÃs e lÃquido/lÃquido), um domÃnio fixo, euleriano, utilizado para discretizar as equaÃÃes de ambas as fases, e outro mÃvel, lagrangiano, usado para as interfaces. Para o presente trabalho, na metologia utilizada, ambos os domÃnios sÃo geometricamente independentes e nÃo apresentam restriÃÃo quanto ao movimento e Ã deformaÃÃo da fase dispersa. Seguindo esta linha, no presente trabalho propÃe-se capturar detalhes deste de tipo escoamento, resolvendo adequadamente as escalas fÃsicas do tempo e do espaÃo, utilizando malhas bloco estruturada refinadas localmente, as quais se adaptam dinamicamente para recobrir as regiÃes de interesse do escoamento (como, por exemplo, ao redor da interface fluido-fluido). Para se obter a resoluÃÃo necessÃria no tempo, Ã usada uma discretiza- ÃÃo semi-implÃcita de segunda ordem para solucionar as equaÃÃes de Navier-Stokes. A modelagem da turbulÃncia Ã introduzida no presente trabalho via SimulaÃÃo de Grandes Escalas. A eficiÃncia e a…

Advisors/Committee Members: Clovis Raimundo Maliska, SolidÃnio Rodrigues de Carvalho, Carlos Henrique Ataide, Aristeu da Silveira Neto, Alexandre Megiorin Roma, Carlos Roberto Ribeiro.

Subjects/Keywords: Turbulence; Adaptive mesh refinement; TurbulÃncia; Multigrid-multilevel; ENGENHARIA MECANICA; Escoamentos multifÃsicos; Mutltiphase flows; Multigrid-multinÃvel; Refinamento local adaptativo

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APA (6^th Edition):

Villar, M. M. (2007). Detailed Two-Dimensional Numerical Analysis of Multiphase Flows. (Thesis). Federal University of Uberlândia. Retrieved from http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Villar, Millena Martins. “Detailed Two-Dimensional Numerical Analysis of Multiphase Flows.” 2007. Thesis, Federal University of Uberlândia. Accessed April 12, 2021. http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Villar, Millena Martins. “Detailed Two-Dimensional Numerical Analysis of Multiphase Flows.” 2007. Web. 12 Apr 2021.

Vancouver:

Villar MM. Detailed Two-Dimensional Numerical Analysis of Multiphase Flows. [Internet] [Thesis]. Federal University of Uberlândia; 2007. [cited 2021 Apr 12]. Available from: http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Villar MM. Detailed Two-Dimensional Numerical Analysis of Multiphase Flows. [Thesis]. Federal University of Uberlândia; 2007. Available from: http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

12. Millena Martins Villar. Análise numérica detalhada de escoamentos multifásicos bidimensionais.

Degree: 2007, Federal University of Uberlândia

URL: http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825

►

The mathematical modeling of multiphase flows involves the interaction between deformable and moving geometries with the fluid in which they are dispersed (immersed). This kind… (more)

▼

The mathematical modeling of multiphase flows involves the interaction between deformable and moving geometries with the fluid in which they are dispersed (immersed). This kind of interaction is present in many practical applications. A common approach to handle these problems is the so called Front-Tracking/Front-Capturing Hybrid Methods. This methodology consists in separating the problem into two domains: an eulerian domain, which is kept fixed and is used to discretize the fluid equations of both phases, and a lagrangian domain, which is used to solve the equations of motion of the interface. Since there is no geometric dependence between these two domains, the method can easily handle moving and deformable interfaces that are dispersed in the flow. Following this line of research, the present work aims to capture accurately details of such flows by resolving adequately the relevant physical scales in time and in space. This can be achieved by applying locally refined meshes which adapt dynamically to cover special flow regions, e.g. the vicinity of the fluid-fluid interfaces. To obtain the required resolution in time, a semi-implicit second order discretization to solve the Navier-Stokes equations is used. The turbulence modeling is introduced in the present work through Large Eddy Simulation. The eficiency and robustness of the methodology applied are verified via convergence analysis, as well as with simulations of one-phase and two-phase flows for several Reynolds numbers. The results of two-phase flows, with one bubble and with multiple bubbles, are presented. The results obtained for a single bubble case are compared with Clift s shape diagram (Clift et al., 1978).

A modelagem matemática de escoamentos multifásicos envolve a interação de geometrias móveis e deformáveis com o meio fluido que as envolve. Este tipo de interação faz parte de uma extensa lista de aplicações. Uma linha proposta para o tratamento num érico deste tipo de problema são os métodos híbridos Front-Tracking/Front-Capturing. Esta abordagem leva à separação do problema em dois domínios distintos (líquido/gás e líquido/líquido), um domínio fixo, euleriano, utilizado para discretizar as equações de ambas as fases, e outro móvel, lagrangiano, usado para as interfaces. Para o presente trabalho, na metologia utilizada, ambos os domínios são geometricamente independentes e não apresentam restrição quanto ao movimento e à deformação da fase dispersa. Seguindo esta linha, no presente trabalho propõe-se capturar detalhes deste de tipo escoamento, resolvendo adequadamente as escalas físicas do tempo e do espaço, utilizando malhas bloco estruturada refinadas localmente, as quais se adaptam dinamicamente para recobrir as regiões de interesse do escoamento (como, por exemplo, ao redor da interface fluido-fluido). Para se obter a resolução necessária no tempo, é usada uma discretização semi-implícita de segunda ordem para solucionar as equações de Navier-Stokes. A modelagem da turbulência é introduzida no presente trabalho via Simulação de Grandes…

Advisors/Committee Members: Solidônio Rodrigues de Carvalho, Aristeu da Silveira Neto, Carlos Roberto Ribeiro, Alexandre Megiorin Roma, Clovis Raimundo Maliska, Carlos Henrique Ataide.

Subjects/Keywords: Multigrid-multinível; ENGENHARIA MECANICA; Escoamentos multifásicos; Turbulência; Refinamento local adaptativo; Adaptive mesh refinement; Mutltiphase flows; Turbulence; Multigrid-multilevel

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Villar, M. M. (2007). Análise numérica detalhada de escoamentos multifásicos bidimensionais. (Thesis). Federal University of Uberlândia. Retrieved from http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Villar, Millena Martins. “Análise numérica detalhada de escoamentos multifásicos bidimensionais.” 2007. Thesis, Federal University of Uberlândia. Accessed April 12, 2021. http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Villar, Millena Martins. “Análise numérica detalhada de escoamentos multifásicos bidimensionais.” 2007. Web. 12 Apr 2021.

Vancouver:

Villar MM. Análise numérica detalhada de escoamentos multifásicos bidimensionais. [Internet] [Thesis]. Federal University of Uberlândia; 2007. [cited 2021 Apr 12]. Available from: http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Villar MM. Análise numérica detalhada de escoamentos multifásicos bidimensionais. [Thesis]. Federal University of Uberlândia; 2007. Available from: http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1821 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1824 ; http://www.bdtd.ufu.br//tde_busca/arquivo.php?codArquivo=1825

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

13. Yang, Zhao, 1983-. A multigrid Krylov method for eigenvalue problems.

Degree: PhD, Baylor University. Dept. of Mathematics., 2015, Baylor University

URL: http://hdl.handle.net/2104/9514

► We are interested in computing eigenvalues and eigenvectors of matrices derived from differential equations. They are often large sparse matrices, including both symmetric and non… (more)

Subjects/Keywords: Krylov subspaces. Arnoldi. Multigrid. Eigenvalue problems.

…Arnoldi method computes the orthogonal projection of A onto an m dimensional Krylov subspace… …Arnoldi method which combines restarted Arnoldi methods and multigrid methods. The dissertation… …Multigrid methods. A Multigrid Arnoldi method will be presented in Chapter Three, followed by some… …Preliminaries The Arnoldi method is a very well-known Krylov subspace method for nonsymmetric… …projection methods(2.1) and Krylov subspaces(2.2). The basic Arnoldi method is…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Yang, Zhao, 1. (2015). A multigrid Krylov method for eigenvalue problems. (Doctoral Dissertation). Baylor University. Retrieved from http://hdl.handle.net/2104/9514

Chicago Manual of Style (16^th Edition):

Yang, Zhao, 1983-. “A multigrid Krylov method for eigenvalue problems.” 2015. Doctoral Dissertation, Baylor University. Accessed April 12, 2021. http://hdl.handle.net/2104/9514.

MLA Handbook (7^th Edition):

Yang, Zhao, 1983-. “A multigrid Krylov method for eigenvalue problems.” 2015. Web. 12 Apr 2021.

Vancouver:

Yang, Zhao 1. A multigrid Krylov method for eigenvalue problems. [Internet] [Doctoral dissertation]. Baylor University; 2015. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/2104/9514.

Council of Science Editors:

Yang, Zhao 1. A multigrid Krylov method for eigenvalue problems. [Doctoral Dissertation]. Baylor University; 2015. Available from: http://hdl.handle.net/2104/9514

14. Köster, Michael. A Hierarchical Flow Solver for Optimisation with PDE Constraints.

Degree: 2011, Technische Universität Dortmund

URL: http://hdl.handle.net/2003/29239

► Active flow control plays a central role in many industrial applications such as e.g. control of crystal growth processes, where the flow in the melt… (more)

▼ Active flow control plays a central role in many industrial applications such as e.g. control of crystal growth processes, where the flow in the melt has a significant impact on the quality of the crystal. Optimal control of the flow by electro-magnetic fields and/or boundary temperatures leads to optimisation problems with PDE constraints, which are frequently governed by the time-dependent Navier-Stokes equations. The mathematical formulation is a minimisation problem with PDE constraints. By exploiting the special structure of the first order necessary optimality conditions, the so called Karush-Kuhn-Tucker (KKT)-system, this thesis develops a special hierarchical solution approach for such equations, based on the distributed control of the Stokes – and Navier – Stokes. The numerical costs for solving the optimisation problem are only about 20-50 times higher than a pure forward simulation, independent of the refinement level. Utilising modern multigrid techniques in space, it is possible to solve a forward simulation with optimal complexity, i.e., an appropriate solver for a forward simulation needs O(N) operations, N denoting the total number of unknowns for a given computational mesh in space and time. Such solvers typically apply appropriate multigrid techniques for the linear subproblems in space. As a consequence, the developed solution approach for the optimal control problem has complexity O(N) as well. This is achieved by a combination of a space-time Newton approach for the nonlinearity and a monolithic space-time multigrid approach for 'global' linear subproblems. A second inner monolithic multigrid method is applied for subproblems in space, utilising local Pressure-Schur complement techniques to treat the saddle-point structure. The numerical complexity of this algorithm distinguishes this approach from adjoint-based steepest descent methods used to solve optimisation problems in many practical applications, which in general do not satisfy this complexity requirement. Advisors/Committee Members: Turek, Stefan.

Subjects/Keywords: Block-Glätter; Block smoother; CFD; Crank-Nicolson; Crystal growth; Czochralski; Distributed Control; Edge-oriented stabilisation; Elliptic; Elliptisch; EOJ stabilisation; EOJ Stabilisierung; FEAT; FEATFLOW; Finite Elemente; Finite Elements; First discretise then optimise; First discretize then optimize; First optimise then discretise; First optimize then discretize; Flow-Around-Cylinder; Full Newton-SAND; Heat equation; Hierarchical; Hierarchical solution concept; Hierarchisch; Hierarchisches Lösungskonzept; Inexact Newton; Inexaktes Newton-Verfahren; Instationär; Inverse Probleme; Inverse Problems; Kantenbasierte Stabilisierung; KKT system; Kristallwachstum; Krylov; Large-Scale; linear complexity; lineare Komplexität; Mehrgitter; Mehrgitter-Krylov; Monolithic; Monolithisch; Multigrid; Multigrid-Krylov; Multilevel; Navier-Stokes; Nichtparametrische Finite Elemente; Nonparametric finite elements; Nonstationary; OPTFLOW; Optimierung; Optimisation; Optimization; PDE Constraints; Raum-Zeit; saddle point; SAND; Sattelpunkt; Schur complement preconditioning; Schurkomplement-Vorkonditionierer; Space-time; SQP; Stokes; Theta schema; Theta scheme; Time-dependent; Transient; Unstructured Grids; Unstrukturierte Gitter; Vanka; Verteilte Kontrolle; Wärmeleitung; Wärmeleitungsgleichung; 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Köster, M. (2011). A Hierarchical Flow Solver for Optimisation with PDE Constraints. (Thesis). Technische Universität Dortmund. Retrieved from http://hdl.handle.net/2003/29239

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Köster, Michael. “A Hierarchical Flow Solver for Optimisation with PDE Constraints.” 2011. Thesis, Technische Universität Dortmund. Accessed April 12, 2021. http://hdl.handle.net/2003/29239.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Köster, Michael. “A Hierarchical Flow Solver for Optimisation with PDE Constraints.” 2011. Web. 12 Apr 2021.

Vancouver:

Köster M. A Hierarchical Flow Solver for Optimisation with PDE Constraints. [Internet] [Thesis]. Technische Universität Dortmund; 2011. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/2003/29239.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Köster M. A Hierarchical Flow Solver for Optimisation with PDE Constraints. [Thesis]. Technische Universität Dortmund; 2011. Available from: http://hdl.handle.net/2003/29239

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

15. Köster, Michael. A Hierarchical Flow Solver for Optimisation with PDE Constraints.

Degree: 2011, Technische Universität Dortmund

URL: http://dx.doi.org/10.17877/DE290R-6950

► Active flow control plays a central role in many industrial applications such as e.g. control of crystal growth processes, where the flow in the melt… (more)

▼ Active flow control plays a central role in many industrial applications such as e.g. control of crystal growth processes, where the flow in the melt has a significant impact on the quality of the crystal. Optimal control of the flow by electro-magnetic fields and/or boundary temperatures leads to optimisation problems with PDE constraints, which are frequently governed by the time-dependent Navier-Stokes equations. The mathematical formulation is a minimisation problem with PDE constraints. By exploiting the special structure of the first order necessary optimality conditions, the so called Karush-Kuhn-Tucker (KKT)-system, this thesis develops a special hierarchical solution approach for such equations, based on the distributed control of the Stokes – and Navier – Stokes. The numerical costs for solving the optimisation problem are only about 20-50 times higher than a pure forward simulation, independent of the refinement level. Utilising modern multigrid techniques in space, it is possible to solve a forward simulation with optimal complexity, i.e., an appropriate solver for a forward simulation needs O(N) operations, N denoting the total number of unknowns for a given computational mesh in space and time. Such solvers typically apply appropriate multigrid techniques for the linear subproblems in space. As a consequence, the developed solution approach for the optimal control problem has complexity O(N) as well. This is achieved by a combination of a space-time Newton approach for the nonlinearity and a monolithic space-time multigrid approach for 'global' linear subproblems. A second inner monolithic multigrid method is applied for subproblems in space, utilising local Pressure-Schur complement techniques to treat the saddle-point structure. The numerical complexity of this algorithm distinguishes this approach from adjoint-based steepest descent methods used to solve optimisation problems in many practical applications, which in general do not satisfy this complexity requirement. Advisors/Committee Members: Turek, Stefan (advisor), Meyer, Christian (referee).

Subjects/Keywords: Block-Glätter; Czochralski; Elliptisch; EOJ Stabilisierung; Finite Elemente; Hierarchisch; Hierarchisches Lösungskonzept; Inexaktes Newton-Verfahren; Instationär; Inverse Probleme; Kantenbasierte Stabilisierung; Kristallwachstum; Krylov; lineare Komplexität; Mehrgitter; Mehrgitter-Krylov; Monolithisch; Navier-Stokes; Nichtparametrische Finite Elemente; Optimierung; Raum-Zeit; Sattelpunkt; Schurkomplement-Vorkonditionierer; Stokes; Unstrukturierte Gitter; Vanka; Verteilte Kontrolle; Wärmeleitung; Wärmeleitungsgleichung; Block smoother; CFD; Crank-Nicolson; Crystal growth; Distributed Control; Edge-oriented stabilisation; Elliptic; EOJ stabilisation; FEAT; FEATFLOW; Finite Elements; First discretise then optimise; First discretize then optimize; First optimise then discretise; First optimize then discretize; Flow-Around-Cylinder; Full Newton-SAND; Heat equation; Hierarchical; Hierarchical solution concept; Inexact Newton; Inverse Problems; KKT system; Large-Scale; linear complexity; Monolithic; Multigrid; Multigrid-Krylov; Multilevel; Nonparametric finite elements; Nonstationary; OPTFLOW; Optimisation; Optimization; PDE Constraints; saddle point; SAND; Schur complement preconditioning; Space-time; SQP; Theta schema; Theta scheme; Time-dependent; Transient; Unstructured Grids; 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Köster, M. (2011). A Hierarchical Flow Solver for Optimisation with PDE Constraints. (Doctoral Dissertation). Technische Universität Dortmund. Retrieved from http://dx.doi.org/10.17877/DE290R-6950

Chicago Manual of Style (16^th Edition):

Köster, Michael. “A Hierarchical Flow Solver for Optimisation with PDE Constraints.” 2011. Doctoral Dissertation, Technische Universität Dortmund. Accessed April 12, 2021. http://dx.doi.org/10.17877/DE290R-6950.

MLA Handbook (7^th Edition):

Köster, Michael. “A Hierarchical Flow Solver for Optimisation with PDE Constraints.” 2011. Web. 12 Apr 2021.

Vancouver:

Köster M. A Hierarchical Flow Solver for Optimisation with PDE Constraints. [Internet] [Doctoral dissertation]. Technische Universität Dortmund; 2011. [cited 2021 Apr 12]. Available from: http://dx.doi.org/10.17877/DE290R-6950.

Council of Science Editors:

Köster M. A Hierarchical Flow Solver for Optimisation with PDE Constraints. [Doctoral Dissertation]. Technische Universität Dortmund; 2011. Available from: http://dx.doi.org/10.17877/DE290R-6950

INP Toulouse

16. Mouffe, Mélodie. Multilevel optimization in infinity norm and associated stopping criteria : Optimisation multiniveaux en norme infinie et critères d’arrêt associés.

Degree: Docteur es, Sciences mathématiques, 2009, INP Toulouse

URL: http://www.theses.fr/2009INPT011G

►

Cette thèse se concentre sur l'étude d'un algorithme multi niveaux de régions de confiance en norme infinie, conçu pour la résolution de problèmes d'optimisation non… (more)

▼

Cette thèse se concentre sur l'étude d'un algorithme multi niveaux de régions de confiance en norme infinie, conçu pour la résolution de problèmes d'optimisation non linéaires de grande taille pouvant être soumis a des contraintes de bornes. L'étude est réalisée tant sur le plan théorique que numérique. L'algorithme RMTR8 que nous étudions ici a été élaboré a partir de l'algorithme présente par Gratton, Sartenaer et Toint (2008b), et modifie d'abord en remplaçant l'usage de la norme Euclidienne par une norme infinie, et ensuite en l'adaptant a la résolution de problèmes de minimisation soumis a des contraintes de bornes. Dans un premier temps, les spécificités du nouvel algorithme sont exposées et discutées. De plus, l'algorithme est démontré globalement convergent au sens de Conn, Gould et Toint (2000), c'est-a-dire convergent vers un minimum local au départ de tout point admissible. D'autre part, il est démontre que la propriété d'identification des contraintes actives des méthodes de régions de confiance basées sur l'utilisation d'un point de Cauchy peut être étendue a tout solveur interne respectant une décroissance suffisante. En conséquence, cette propriété d'identification est aussi respectée par une variante particulière du nouvel algorithme. Par la suite, nous étudions différents critères d'arrêt pour les algorithmes d'optimisation avec contraintes de bornes afin de déterminer le sens et les avantages de chacun, et ce pour pouvoir choisir aisément celui qui convient le mieux a certaines situations. En particulier, les critères d'arrêts sont analyses en termes d'erreur inverse (backward erreur), tant au sens classique du terme (avec l'usage d'une norme produit) que du point de vue de l'optimisation multicritères. Enfin, un algorithme pratique est mis en place, utilisant en particulier une technique similaire au lissage de Gauss-Seidel comme solveur interne. Des expérimentations numériques sont réalisées sur une version FORTRAN 95 de l'algorithme. Elles permettent d'une part de définir un panel de paramètres efficaces par défaut et, d'autre part, de comparer le nouvel algorithme a d'autres algorithmes classiques d'optimisation, comme la technique de raffinement de maillage ou la méthode du gradient conjugue, sur des problèmes avec et sans contraintes de bornes. Ces comparaisons numériques semblent donner l'avantage à l'algorithme multi niveaux, en particulier sur les cas peu non-linéaires, comportement attendu de la part d'un algorithme inspire des techniques multi grilles. En conclusion, l'algorithme de région de confiance multi niveaux présente dans cette thèse est une amélioration du précédent algorithme de cette classe d'une part par l'usage de la norme infinie et d'autre part grâce a son traitement de possibles contraintes de bornes. Il est analyse tant sur le plan de la convergence que de son comportement vis-à-vis des bornes, ou encore de la définition de son critère d'arrêt. Il montre en outre un comportement numérique prometteur.

This thesis concerns the study of a multilevel trust-region algorithm…

Advisors/Committee Members: Gratton, Serge (thesis director), Toint, Philippe (thesis director).

Subjects/Keywords: Nonconvex optimization; Multigrid; Multilevel methods; Trust-region methods; Convergence theory; Bound constraints

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mouffe, M. (2009). Multilevel optimization in infinity norm and associated stopping criteria : Optimisation multiniveaux en norme infinie et critères d’arrêt associés. (Doctoral Dissertation). INP Toulouse. Retrieved from http://www.theses.fr/2009INPT011G

Chicago Manual of Style (16^th Edition):

Mouffe, Mélodie. “Multilevel optimization in infinity norm and associated stopping criteria : Optimisation multiniveaux en norme infinie et critères d’arrêt associés.” 2009. Doctoral Dissertation, INP Toulouse. Accessed April 12, 2021. http://www.theses.fr/2009INPT011G.

MLA Handbook (7^th Edition):

Mouffe, Mélodie. “Multilevel optimization in infinity norm and associated stopping criteria : Optimisation multiniveaux en norme infinie et critères d’arrêt associés.” 2009. Web. 12 Apr 2021.

Vancouver:

Mouffe M. Multilevel optimization in infinity norm and associated stopping criteria : Optimisation multiniveaux en norme infinie et critères d’arrêt associés. [Internet] [Doctoral dissertation]. INP Toulouse; 2009. [cited 2021 Apr 12]. Available from: http://www.theses.fr/2009INPT011G.

Council of Science Editors:

Mouffe M. Multilevel optimization in infinity norm and associated stopping criteria : Optimisation multiniveaux en norme infinie et critères d’arrêt associés. [Doctoral Dissertation]. INP Toulouse; 2009. Available from: http://www.theses.fr/2009INPT011G

17. Badahmane, Achraf. Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides.

Degree: Docteur es, Mathématiques. Mathématiques appliquées, 2019, Littoral; Université Cadi Ayyad (Marrakech, Maroc)

URL: http://www.theses.fr/2019DUNK0543

►

La résolution numérique des problèmes de point-selle a eu une attention particulière ces dernières années. À titre d'exemple, la mécanique des fluides et solides conduit… (more)

Subjects/Keywords: Point-selle; Préconditionnement; Krylov; Produit de Kronecker; Produit de diamant; Saddle point; Preconditioner; Global Krylov subspace method; Kronecker product; Diamond product

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Badahmane, A. (2019). Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides. (Doctoral Dissertation). Littoral; Université Cadi Ayyad (Marrakech, Maroc). Retrieved from http://www.theses.fr/2019DUNK0543

Chicago Manual of Style (16^th Edition):

Badahmane, Achraf. “Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides.” 2019. Doctoral Dissertation, Littoral; Université Cadi Ayyad (Marrakech, Maroc). Accessed April 12, 2021. http://www.theses.fr/2019DUNK0543.

MLA Handbook (7^th Edition):

Badahmane, Achraf. “Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides.” 2019. Web. 12 Apr 2021.

Vancouver:

Badahmane A. Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides. [Internet] [Doctoral dissertation]. Littoral; Université Cadi Ayyad (Marrakech, Maroc); 2019. [cited 2021 Apr 12]. Available from: http://www.theses.fr/2019DUNK0543.

Council of Science Editors:

Badahmane A. Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides. [Doctoral Dissertation]. Littoral; Université Cadi Ayyad (Marrakech, Maroc); 2019. Available from: http://www.theses.fr/2019DUNK0543

Delft University of Technology

18. Bin Zubair, H. Efficient Multigrid Methods based on Improved Coarse Grid Correction Techniques.

Degree: 2009, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; urn:NBN:nl:ui:24-uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; urn:NBN:nl:ui:24-uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; http://resolver.tudelft.nl/uuid:e0b43b38-ad07-4076-baf1-aa02579c397f

► Multigrid efficiency often suffers from inadequate coarse grid correction in different prototypic situations. We select a few problems, where coarse grid correction issues arise because… (more)

▼ Multigrid efficiency often suffers from inadequate coarse grid correction in different prototypic situations. We select a few problems, where coarse grid correction issues arise because of anisotropic coefficients, non-equidistant or non-uniform grid stretching, or inherent indefiniteness in the partial differential equation. Most of the work in this thesis can be classified as an attempt to increase multigrid efficiency by analysing and developing novel grid coarsening techniques that ensure sufficient coarse grid correction for the multigrid algorithm. Anisotropy in discrete systems can stem from various continuous and discrete features of the problem and has to have its negative effects countered before a successful multigrid solution can be brought about. We select multidimensional stationary diffusion equation as the first important problem to be treated in this context. The work for dimensions higher than three, is aimed at developing grid coarsening strategies for discretization on rectangular hyper-grids that differ greatly in their dimensions, and thus induce the so-called grid-aligned anisotropies in the system. Coarse grids formed through standard coarsening fail to provide sufficient coarse grid correction, and alternative block relaxation techniques are expensive in high dimensions. We also investigate and test coarsening strategies with the aim that their use would allow point based relaxation to stay effective in this non-equidistant multigrid scenario. Through local Fourier analysis we also analyze w-RB Jacobi, and implement a computer program through which we compute the optimal relaxation parameters. There are three important inferences in this regard. (1) Partial (and grid dependent) coarsening strategies allow the successful use of point relaxation methods for this problem. (2) Quadrupling along a few dimensions is a very attractive partial coarsening choice. (3) Optimal relaxation parameters have a significant enhancement effect on multigrid convergence in high dimensions. The efficient solution of time-dependent multidimensional equations (discretized with implicit time-integration schemes) is also a challenge. We first use the sparse grid technique to reduce the exponential complexity of the discrete problem, and then use the d-dimensional multigrid techniques to solve the sparse grid sub problems. In this situation, i.e., with a multitude of different non equidistant grids, evaluating and using optimal relaxation parameters on the fly is not an option any more. As a multigrid solver in high dimensions depends on optimal attributes to quite a large extent, we employ the method as a preconditioner, instead of a solver. This results in a very robust and efficient multigrid preconditioned Bi-CGSTAB solver. Another coarsening strategy that we develop in this thesis is aimed at two-dimensional grids that are non-uniformly stretched. We investigated different experimental coarsening strategies. A strategy based on improving individual mesh aspect ratios of grid cells proves successful both… Advisors/Committee Members: Oosterlee, C.W..

Subjects/Keywords: multigrid; d-multigrid; sparse grids; multidimensional partial differential equations; multigrid preconditioned Krylov methods; grid-stretching; indefinite Helmholtz; adaptive mesh-refinement

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Bin Zubair, H. (2009). Efficient Multigrid Methods based on Improved Coarse Grid Correction Techniques. (Doctoral Dissertation). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; urn:NBN:nl:ui:24-uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; urn:NBN:nl:ui:24-uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; http://resolver.tudelft.nl/uuid:e0b43b38-ad07-4076-baf1-aa02579c397f

Chicago Manual of Style (16^th Edition):

Bin Zubair, H. “Efficient Multigrid Methods based on Improved Coarse Grid Correction Techniques.” 2009. Doctoral Dissertation, Delft University of Technology. Accessed April 12, 2021. http://resolver.tudelft.nl/uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; urn:NBN:nl:ui:24-uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; urn:NBN:nl:ui:24-uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; http://resolver.tudelft.nl/uuid:e0b43b38-ad07-4076-baf1-aa02579c397f.

MLA Handbook (7^th Edition):

Bin Zubair, H. “Efficient Multigrid Methods based on Improved Coarse Grid Correction Techniques.” 2009. Web. 12 Apr 2021.

Vancouver:

Bin Zubair H. Efficient Multigrid Methods based on Improved Coarse Grid Correction Techniques. [Internet] [Doctoral dissertation]. Delft University of Technology; 2009. [cited 2021 Apr 12]. Available from: http://resolver.tudelft.nl/uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; urn:NBN:nl:ui:24-uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; urn:NBN:nl:ui:24-uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; http://resolver.tudelft.nl/uuid:e0b43b38-ad07-4076-baf1-aa02579c397f.

Council of Science Editors:

Bin Zubair H. Efficient Multigrid Methods based on Improved Coarse Grid Correction Techniques. [Doctoral Dissertation]. Delft University of Technology; 2009. Available from: http://resolver.tudelft.nl/uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; urn:NBN:nl:ui:24-uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; urn:NBN:nl:ui:24-uuid:e0b43b38-ad07-4076-baf1-aa02579c397f ; http://resolver.tudelft.nl/uuid:e0b43b38-ad07-4076-baf1-aa02579c397f

19. El-Borhamy, Mohamed. Numerical simulation for viscoplastic fluids via finite element methods.

Degree: 2012, Technische Universität Dortmund

URL: http://hdl.handle.net/2003/29415

► The design of eﬃcient, robust and ﬂexible numerical schemes to cope with nonlinear CFD problems has become the main nerve in the ﬁeld of numerical… (more)

▼ The design of eﬃcient, robust and ﬂexible numerical schemes to cope with nonlinear CFD problems has become the main nerve in the ﬁeld of numerical simulation. This work has developed and analyzed the Newton-Multigrid process in the frame of monolithic approaches to solve stationary and nonstationary viscoplastic ﬂuid problems. From the mathematical point of view, the viscoplastic problem exhibits several severe problems which might be arisen to draw the mathematical challenges. The major diﬃculty is the unbounded value of the viscosity which needs regularization. Several regularization techniques have been proposed to cope with this problem yet, while the accuracy is still not even close to be compared to the real model. Herein, two methods are used for the treatment of the non-differentiability, namely Bercovier-Engelman and modiﬁed bi-viscous models regularizations. To compute the solution at very small values of the regularization parameter which can be considered numerically as zero, we use the continuation technique. Other diﬃculties would be addressed in the circle of the nonlinearity, the solenoidal velocity ﬁeld, as well as the convection dominated problem which are typically involved in the standard Navier-Stokes equation. The use of mixed higher order ﬁnite element methods for ﬂow problems is advantageous, since one can partially avoid the addition of stabilization terms to handle for instance the lack of coercivity, the domination of the convective part as well as the incompressibility. In the case of mixed lower order ﬁnite element methods, edge oriented stabilization has been introduced to provide results in the case of the lack of coercivity and convection dominated problems. The main drawback of this stabilizer is to optimize or choose appropriately the free parameters to maintain high accuracy results from the scheme. Viscoplastic ﬂuids are involved in many industrial applications which require numerical simulation to get a big mathematical insight and to predict the ﬂuids behavior. The dependence of pressure on the viscoplastic constitutive law is conﬁrmed as much as the dependence of velocity. Moreover, the behavior of the pressure is strongly related to the yield property for the unyielded regimes. In the case of a constant yield stress value together with the absence of the external densities, the ﬁeld of pressure is prescribed by the null value wherever the null value of the deformation tensor is considered. Real life examples to prescribe the behavior of the viscoplastic ﬂuids might be described in case of standard benchmarks: viscoplastic ﬂow in channel, viscoplastic ﬂow in a lid driven cavity and viscoplastic ﬂow around a cylinder. In each case we conﬁrm the experimental and theoretical results which are used to analyze viscoplastic problems for the physical behavior with respect to the unyielded regimes and the cessation of time. Advisors/Committee Members: Turek, Stefan.

Subjects/Keywords: finite element method; multigrid method; Newton method; time stepping schemes; viscoplastic fluids; 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

El-Borhamy, M. (2012). Numerical simulation for viscoplastic fluids via finite element methods. (Thesis). Technische Universität Dortmund. Retrieved from http://hdl.handle.net/2003/29415

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

El-Borhamy, Mohamed. “Numerical simulation for viscoplastic fluids via finite element methods.” 2012. Thesis, Technische Universität Dortmund. Accessed April 12, 2021. http://hdl.handle.net/2003/29415.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

El-Borhamy, Mohamed. “Numerical simulation for viscoplastic fluids via finite element methods.” 2012. Web. 12 Apr 2021.

Vancouver:

El-Borhamy M. Numerical simulation for viscoplastic fluids via finite element methods. [Internet] [Thesis]. Technische Universität Dortmund; 2012. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/2003/29415.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

El-Borhamy M. Numerical simulation for viscoplastic fluids via finite element methods. [Thesis]. Technische Universität Dortmund; 2012. Available from: http://hdl.handle.net/2003/29415

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

20. El-Borhamy, Mohamed. Numerical simulation for viscoplastic fluids via finite element methods.

Degree: 2012, Technische Universität Dortmund

URL: http://dx.doi.org/10.17877/DE290R-3283

► The design of eﬃcient, robust and ﬂexible numerical schemes to cope with nonlinear CFD problems has become the main nerve in the ﬁeld of numerical… (more)

▼ The design of eﬃcient, robust and ﬂexible numerical schemes to cope with nonlinear CFD problems has become the main nerve in the ﬁeld of numerical simulation. This work has developed and analyzed the Newton-Multigrid process in the frame of monolithic approaches to solve stationary and nonstationary viscoplastic ﬂuid problems. From the mathematical point of view, the viscoplastic problem exhibits several severe problems which might be arisen to draw the mathematical challenges. The major diﬃculty is the unbounded value of the viscosity which needs regularization. Several regularization techniques have been proposed to cope with this problem yet, while the accuracy is still not even close to be compared to the real model. Herein, two methods are used for the treatment of the non-differentiability, namely Bercovier-Engelman and modiﬁed bi-viscous models regularizations. To compute the solution at very small values of the regularization parameter which can be considered numerically as zero, we use the continuation technique. Other diﬃculties would be addressed in the circle of the nonlinearity, the solenoidal velocity ﬁeld, as well as the convection dominated problem which are typically involved in the standard Navier-Stokes equation. The use of mixed higher order ﬁnite element methods for ﬂow problems is advantageous, since one can partially avoid the addition of stabilization terms to handle for instance the lack of coercivity, the domination of the convective part as well as the incompressibility. In the case of mixed lower order ﬁnite element methods, edge oriented stabilization has been introduced to provide results in the case of the lack of coercivity and convection dominated problems. The main drawback of this stabilizer is to optimize or choose appropriately the free parameters to maintain high accuracy results from the scheme. Viscoplastic ﬂuids are involved in many industrial applications which require numerical simulation to get a big mathematical insight and to predict the ﬂuids behavior. The dependence of pressure on the viscoplastic constitutive law is conﬁrmed as much as the dependence of velocity. Moreover, the behavior of the pressure is strongly related to the yield property for the unyielded regimes. In the case of a constant yield stress value together with the absence of the external densities, the ﬁeld of pressure is prescribed by the null value wherever the null value of the deformation tensor is considered. Real life examples to prescribe the behavior of the viscoplastic ﬂuids might be described in case of standard benchmarks: viscoplastic ﬂow in channel, viscoplastic ﬂow in a lid driven cavity and viscoplastic ﬂow around a cylinder. In each case we conﬁrm the experimental and theoretical results which are used to analyze viscoplastic problems for the physical behavior with respect to the unyielded regimes and the cessation of time. Advisors/Committee Members: Turek, Stefan (advisor), Blum, Heribert (referee).

Subjects/Keywords: finite element method; multigrid method; Newton method; time stepping schemes; viscoplastic fluids; 510

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

El-Borhamy, M. (2012). Numerical simulation for viscoplastic fluids via finite element methods. (Doctoral Dissertation). Technische Universität Dortmund. Retrieved from http://dx.doi.org/10.17877/DE290R-3283

Chicago Manual of Style (16^th Edition):

El-Borhamy, Mohamed. “Numerical simulation for viscoplastic fluids via finite element methods.” 2012. Doctoral Dissertation, Technische Universität Dortmund. Accessed April 12, 2021. http://dx.doi.org/10.17877/DE290R-3283.

MLA Handbook (7^th Edition):

El-Borhamy, Mohamed. “Numerical simulation for viscoplastic fluids via finite element methods.” 2012. Web. 12 Apr 2021.

Vancouver:

El-Borhamy M. Numerical simulation for viscoplastic fluids via finite element methods. [Internet] [Doctoral dissertation]. Technische Universität Dortmund; 2012. [cited 2021 Apr 12]. Available from: http://dx.doi.org/10.17877/DE290R-3283.

Council of Science Editors:

El-Borhamy M. Numerical simulation for viscoplastic fluids via finite element methods. [Doctoral Dissertation]. Technische Universität Dortmund; 2012. Available from: http://dx.doi.org/10.17877/DE290R-3283

21. Ul Jabbar, Absaar. Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations.

Degree: 2018, Technische Universität Dortmund

URL: http://dx.doi.org/10.17877/DE290R-19859

► Multigrid methods belong to the best-known methods for solving linear systems arising from the discretization of elliptic partial differential equations. The main attraction of multigrid… (more)

▼ Multigrid methods belong to the best-known methods for solving linear systems arising from the discretization of elliptic partial differential equations. The main attraction of multigrid methods is that they have an asymptotically meshindependent convergence behavior. Multigrid with Vanka (or local multilevel pressure Schur complement method) as smoother have been frequently used for the construction of very effcient coupled monolithic solvers for the solution of the stationary incompressible Navier-Stokes equations in 2D and 3D. However, due to its innate Gauß-Seidel/Jacobi character, Vanka has a strong influence of the underlying mesh, and therefore, coupled multigrid solvers with Vanka smoothing very frequently face convergence issues on meshes with high aspect ratios. Moreover, even on very nice regular grids, these solvers may fail when the anisotropies are introduced from the differential operator. In this thesis, we develop a new class of robust and efficient monolithic finite element multilevel Krylov subspace methods (MLKM) for the solution of the stationary incompressible Navier-Stokes equations as an alternative to the coupled multigrid-based solvers. Different from multigrid, the MLKM utilizes a Krylov method as the basis in the error reduction process. The solver is based on the multilevel projection-based method of Erlangga and Nabben, which accelerates the convergence of the Krylov subspace methods by shifting the small eigenvalues of the system matrix, responsible for the slow convergence of the Krylov iteration, to the largest eigenvalue. Before embarking on the Navier-Stokes equations, we first test our implementation of the MLKM solver by solving scalar model problems, namely the convection-diffusion problem and the anisotropic diffusion problem. We validate the method by solving several standard benchmark problems. Next, we present the numerical results for the solution of the incompressible Navier-Stokes equations in two dimensions. The results show that the MLKM solvers produce asymptotically mesh-size independent, as well as Reynolds number independent convergence rates, for a moderate range of Reynolds numbers. Moreover, numerical simulations also show that the coupled MLKM solvers can handle (both mesh and operator based) anisotropies better than the coupled multigrid solvers. Advisors/Committee Members: Turek, Stefan (advisor), Blum, Heribert (referee).

Subjects/Keywords: Monolithic multilevel methods; Krylov subspaces; GMRES; FEM; Navier-Stokes equations; Saddle point problems; 510; Multi-level-Verfahren; Krylov-Verfahren; Finite-Elemente-Methode; Navier-Stokes-Gleichung

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ul Jabbar, A. (2018). Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations. (Doctoral Dissertation). Technische Universität Dortmund. Retrieved from http://dx.doi.org/10.17877/DE290R-19859

Chicago Manual of Style (16^th Edition):

Ul Jabbar, Absaar. “Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations.” 2018. Doctoral Dissertation, Technische Universität Dortmund. Accessed April 12, 2021. http://dx.doi.org/10.17877/DE290R-19859.

MLA Handbook (7^th Edition):

Ul Jabbar, Absaar. “Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations.” 2018. Web. 12 Apr 2021.

Vancouver:

Ul Jabbar A. Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations. [Internet] [Doctoral dissertation]. Technische Universität Dortmund; 2018. [cited 2021 Apr 12]. Available from: http://dx.doi.org/10.17877/DE290R-19859.

Council of Science Editors:

Ul Jabbar A. Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations. [Doctoral Dissertation]. Technische Universität Dortmund; 2018. Available from: http://dx.doi.org/10.17877/DE290R-19859

22. Pogulis, Markus. Algebraic multigrid for a mass-consistent wind model, the Nordic Urban Dispersion model.

Degree: Physics, 2015, Umeå University

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-105499

► In preparation for, and for decision support during, CBRN (chemical, biological, radiological and nuclear) emergencies it is essential to know how such an event… (more)

▼ In preparation for, and for decision support during, CBRN (chemical, biological, radiological and nuclear) emergencies it is essential to know how such an event would turn out, so that one can prepare a possible evacuation. Afterwards it might be good to know how to backtrack and see what caused the emergency, and in the case of e.g. a gas leak, where did it begin? The Swedish Defence Research Agency (FOI) develops models for such scenarios. In this thesis FOI's model, "The Nordic Urban Dispersion model" (NUD), has been studied. The system of equations set up by this model was originally solved using Intel's PARDISO solver, which is a direct solver. An evaluation on how an iterative multigrid method would work to solve the system has been done in this thesis. The wind model is a mass-consistent model which sets up a diagnostic initial wind field. The final wind field is later minimized under the constraint of the continuity equation. The minimization problem is solved using Lagrange multipliers and the system turns into a Poisson-like problem. The iterative algebraic multigrid solver (AMG) which has been evaluated had difficulties solving the problem of an asymmetric system matrix generated by NUD. The AMG solver was then tried on a symmetric discrete Poisson problem instead, and the solution turns out to be the same as for the PARDISO solver. A comparison was made between the AMG and PARDISO solver, and for the discrete Poisson case the AMG solver turned out on top for both larger system size and less computational time. To try out the solvers for the original NUD case a modification of the boundary conditions was made to make the system matrix symmetric. This modification turns the problem into a mathematical problem rather than a physical one, as the wind fields generated are not physically correct. For this modified case both the solvers get the same solution in essentially the same computational time. A method of how to in the future solve the original (asymmetric) problem, by modifying the discretization of the boundary conditions, has been discussed.

Subjects/Keywords: Mass-consistent model; urban environment; numerical method; algebraic multigrid

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Pogulis, M. (2015). Algebraic multigrid for a mass-consistent wind model, the Nordic Urban Dispersion model. (Thesis). Umeå University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-105499

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Pogulis, Markus. “Algebraic multigrid for a mass-consistent wind model, the Nordic Urban Dispersion model.” 2015. Thesis, Umeå University. Accessed April 12, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-105499.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Pogulis, Markus. “Algebraic multigrid for a mass-consistent wind model, the Nordic Urban Dispersion model.” 2015. Web. 12 Apr 2021.

Vancouver:

Pogulis M. Algebraic multigrid for a mass-consistent wind model, the Nordic Urban Dispersion model. [Internet] [Thesis]. Umeå University; 2015. [cited 2021 Apr 12]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-105499.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Pogulis M. Algebraic multigrid for a mass-consistent wind model, the Nordic Urban Dispersion model. [Thesis]. Umeå University; 2015. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-105499

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Minnesota

23. Osei-Kuffuor, Danie. Robust preconditioning for indefnite and Ill-conditioned sparse linear systems.

Degree: PhD, Scientific Computation, 2011, University of Minnesota

URL: http://purl.umn.edu/119987

► Linear systems originating from certain applications in the physical sciences can be challenging to solve by iterative methods. In the past, direct methods like Gaussian… (more)

▼ Linear systems originating from certain applications in the physical sciences can be challenging to solve by iterative methods. In the past, direct methods like Gaussian elimination have been often used to solve these systems, due to their robust nature. However, as problems are now often formulated in 3-D geometries, the use of direct solvers is becoming prohibitive. Moreover, unlike iterative solvers, direct solvers cannot be easily parallelized. Two classes of methods have attracted the interest of researchers in recent years. First, is the class of multigrid methods, which have been shown to be very efficient for elliptic-type problems, and for which various adaptations have been brought. Second, is the class of preconditioned Krylov subspace methods. Here, work has focused mainly on improving the preconditioning. The underlying challenge is to develop or identify techniques that are robust and efficient in terms of accuracy, stability, and scalability. As problems in computational science continue to evolve, so do preconditioning techniques, as new ideas are incorporated to develop solver technologies that are well adapted to solve novel and challenging problems. To further contribute to this endeavor, my research uses ideas from numerical linear algebra to address algorithmic and computational issues in the numerical solution of application problems. The ideas presented in this thesis will focus on improving the stability and effectiveness of ILU-based preconditioners to better handle challenging problems characterized by indefinite and poorly conditioned linear systems. First, we present various strategies designed to improve the quality of the ILU factorization in order to safeguard stability without compromising the accuracy of the resulting factors. These strategies introduce new contributions to the areas of shifted ILU methods, modified ILU and compensation-based techniques, and reordering techniques for ILU. The resulting factors yield good and more robust preconditioners that are effective on highly indefinite and ill-conditioned linear systems. Next, we demonstrate the effectiveness of combining ILU factorizations with multilevel methods. Multilevel ILU methods have become a popular area of research, as researchers seek to take advantage of the superior robustness of ILU, coupled with the efficiency and scalability of multilevel methods. We discuss issues related to constructing the next-level matrices in the multilevel hierarchy and present ideas from multilevel graph coarsening and reordering strategies to construct an algebraic multilevel ILU-based preconditioner. Finally, we discuss key concepts necessary for an efficient adaptation of the ILU-based preconditioner into a parallel framework. We discuss the parallel implementation within the structure of the parallel algebraic multilevel solver (pARMS) framework. We demonstrate how different preconditioning techniques may be incorporated into this framework, and discuss issues relating to scalability.

Subjects/Keywords: Algebraic preconditioners; Incomplete factorization preconditioners; Indefinite linear systems; Multilevel preconditioners; Parallel preconditioners; Preconditioned Krylov methods; Scientific Computation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Osei-Kuffuor, D. (2011). Robust preconditioning for indefnite and Ill-conditioned sparse linear systems. (Doctoral Dissertation). University of Minnesota. Retrieved from http://purl.umn.edu/119987

Chicago Manual of Style (16^th Edition):

Osei-Kuffuor, Danie. “Robust preconditioning for indefnite and Ill-conditioned sparse linear systems.” 2011. Doctoral Dissertation, University of Minnesota. Accessed April 12, 2021. http://purl.umn.edu/119987.

MLA Handbook (7^th Edition):

Osei-Kuffuor, Danie. “Robust preconditioning for indefnite and Ill-conditioned sparse linear systems.” 2011. Web. 12 Apr 2021.

Vancouver:

Osei-Kuffuor D. Robust preconditioning for indefnite and Ill-conditioned sparse linear systems. [Internet] [Doctoral dissertation]. University of Minnesota; 2011. [cited 2021 Apr 12]. Available from: http://purl.umn.edu/119987.

Council of Science Editors:

Osei-Kuffuor D. Robust preconditioning for indefnite and Ill-conditioned sparse linear systems. [Doctoral Dissertation]. University of Minnesota; 2011. Available from: http://purl.umn.edu/119987

Brno University of Technology

24. Sýkora, Ota. Návrh uživatelského rozhraní pro simulaci dějů v EHD mazaných kontaktech: User interface design of software application for simulation of EHD problems.

Degree: 2019, Brno University of Technology

URL: http://hdl.handle.net/11012/33105

► This bachelor thesis deals with the design and implementation of user interface of software application for simulation of elastohydrodynamic lubrication (EHL) problems. The first part… (more)

Subjects/Keywords: elastohydrodynamické mazání; multigrid metoda; uživatelské prostředí; Qt Creator; elastohydrodynamic lubrication; multigrid method; user interface; Qt Creator

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Sýkora, O. (2019). Návrh uživatelského rozhraní pro simulaci dějů v EHD mazaných kontaktech: User interface design of software application for simulation of EHD problems. (Thesis). Brno University of Technology. Retrieved from http://hdl.handle.net/11012/33105

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Sýkora, Ota. “Návrh uživatelského rozhraní pro simulaci dějů v EHD mazaných kontaktech: User interface design of software application for simulation of EHD problems.” 2019. Thesis, Brno University of Technology. Accessed April 12, 2021. http://hdl.handle.net/11012/33105.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Sýkora, Ota. “Návrh uživatelského rozhraní pro simulaci dějů v EHD mazaných kontaktech: User interface design of software application for simulation of EHD problems.” 2019. Web. 12 Apr 2021.

Vancouver:

Sýkora O. Návrh uživatelského rozhraní pro simulaci dějů v EHD mazaných kontaktech: User interface design of software application for simulation of EHD problems. [Internet] [Thesis]. Brno University of Technology; 2019. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/11012/33105.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sýkora O. Návrh uživatelského rozhraní pro simulaci dějů v EHD mazaných kontaktech: User interface design of software application for simulation of EHD problems. [Thesis]. Brno University of Technology; 2019. Available from: http://hdl.handle.net/11012/33105

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Universidade Estadual de Campinas

25. Ramos, Leandro Ito, 1990-. Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial.

Degree: Faculdade de Engenharia Mecânica; Programa de Pós-Graduação em Engenharia Mecânica, 2018, Universidade Estadual de Campinas

URL: RAMOS, Leandro Ito. Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. 2018. 1 recurso online (119 p.). Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/331142>. Acesso em: 3 set. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/331142

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Orientador: Gregory Bregion Daniel

Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica

Made available in DSpace on 2018-09-03T09:22:52Z (GMT). No. of bitstreams:… (more)

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Orientador: Gregory Bregion Daniel

Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica

Made available in DSpace on 2018-09-03T09:22:52Z (GMT). No. of bitstreams: 1 Ramos_LeandroIto_M.pdf: 6462078 bytes, checksum: bec1cda289b67bf3c4dbf72ad1a2dc0a (MD5) Previous issue date: 2018

Resumo: É crescente a demanda por máquinas e equipamentos mais eficientes quanto ao consumo energético, uma vez que as legislações ambiental e de eficiência energética têm pressionado de forma crescente os fabricantes das mesmas. Neste contexto, o mancal hidrodinâmico radial apresenta-se como um componente de máquinas rotativas com grandes oportunidades de melhoria de projeto para redução da energia dissipada em seu fluido lubrificante. Recentemente a texturização da superfície interna de mancais tem sido uma abordagem explorada no intuito de alcançar melhorias não somente nesta dissipação viscosa como também na sustentação hidrodinâmica no componente. Assim, o objetivo do presente trabalho foi desenvolver códigos computacionais eficientes para investigação do efeito da inserção de texturas na superfície de mancais hidrodinâmicos sobre seu funcionamento, definindo ainda parâmetros adequados de texturização para as condições estática e dinâmica de carregamento do componente. Para tanto, a equação clássica de Reynolds com condição de fronteira de cavitação de Swift-Stieber foi adotada e sua discretização foi realizada pela aplicação do Método dos Volumes Finitos (MVF). O sistema de equações resultante é resolvido por um algoritmo Full Multigrid (FMG). Foram estudados os valores mais adequados para os parâmetros da técnica numérica de multiníveis para, em seguida, explorar os efeitos das texturizações parcial e total da superfície do mancal sobre suas principais características estáticas. Os resultados mostram a necessidade por uma seleção adequada principalmente do número de níveis utilizados na técnica multiníveis de modo que mesmo o nível com a malha mais grosseira ainda seja capaz de detectar com nitidez as texturas na superfície do componente. As simulações com mancais texturizados em condição estática de carregamento mostraram que as condições de operação influenciam de forma significativa os efeitos dos parâmetros de texturas, para as texturizações completa e parcial, e que é possível obter ganho de sustentação e/ou redução da perda viscosa no componente através dos adequados posicionamento e especificação das características geométricas das texturas. Mancais com texturizações projetadas em condição estática de carregamento mantêm as melhorias atingidas na sustentação hidrodinâmica e/ou dissipação viscosa quando empregados em sistemas rotativos com pequeno desbalanceamento de massa

The demand for more efficient machines and equipment regarding energy consumption is growing since environmental and energy efficiency legislations have increasingly pressured their manufacturers. In this context, the radial hydrodynamic bearing is a component of rotary machines with great opportunities for…

Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS, Daniel, Gregory Bregion, 1984-, Bittencourt, Marco Lúcio, Bavastri, Carlos Alberto.

Subjects/Keywords: Mancais; Textura; Métodos multigrid (Análise numérica); Método dos volumes finitos; Bearings; Texture; Multigrid methods (Numerical analysis); Finite volume method

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ramos, Leandro Ito, 1. (2018). Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. (Masters Thesis). Universidade Estadual de Campinas. Retrieved from RAMOS, Leandro Ito. Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. 2018. 1 recurso online (119 p.). Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/331142>. Acesso em: 3 set. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/331142

Chicago Manual of Style (16^th Edition):

Ramos, Leandro Ito, 1990-. “Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial.” 2018. Masters Thesis, Universidade Estadual de Campinas. Accessed April 12, 2021. RAMOS, Leandro Ito. Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. 2018. 1 recurso online (119 p.). Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/331142>. Acesso em: 3 set. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/331142.

MLA Handbook (7^th Edition):

Ramos, Leandro Ito, 1990-. “Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial.” 2018. Web. 12 Apr 2021.

Vancouver:

Ramos, Leandro Ito 1. Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. [Internet] [Masters thesis]. Universidade Estadual de Campinas; 2018. [cited 2021 Apr 12]. Available from: RAMOS, Leandro Ito. Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. 2018. 1 recurso online (119 p.). Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/331142>. Acesso em: 3 set. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/331142.

Council of Science Editors:

Ramos, Leandro Ito 1. Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. [Masters Thesis]. Universidade Estadual de Campinas; 2018. Available from: RAMOS, Leandro Ito. Modelagem de mancais hidrodinâmicos com efeitos de texturização superficial. 2018. 1 recurso online (119 p.). Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/331142>. Acesso em: 3 set. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/331142

26. Anca, Dan. Fictitious boundary and penalization methods for treatment of rigid objects in incompressible flows.

Degree: 2014, Technische Universität Dortmund

URL: http://dx.doi.org/10.17877/DE290R-15342

► The Fictitious Boundary Method (FBM) and the Penalty Method (PM) for solving the incompressible Navier-Stokes equations modeling steady or unsteady incompressible flow around solid and… (more)

▼ The Fictitious Boundary Method (FBM) and the Penalty Method (PM) for solving the incompressible Navier-Stokes equations modeling steady or unsteady incompressible flow around solid and rigid, non-deformable objects are presented and numerically analyzed and compared in this thesis. The proposed methods are finite element methods to simulate incompressible flows with small-scale time-(in)dependent geometrical details. The FBM, described and already validated in [1, 43, 48], is based on a finite element method background grid which covers the whole computational domain and is independent of the shape, number and size of any solid obstacle contained inside. The fluid part is computed by a multigrid finite element solver, while the behavior of the solid part is governed by the mechanics principles regarding motion and interactions of type fluid-solid, solid-solid or solid-wall collisions. A new treatment of imposing the Dirichlet boundary conditions for the case of immersed rigid boundary objects is proposed by using the penalization method as a more general framework then the FBM, but containing it as a special case. The new PM approach has a stronger mathematical background. In contrast to FBM, the PM does not imply a direct modification or artificial techniques over the matrix of the system of equations like the fictitious boundary method. A pairing of the penalty method with multigrid solvers is used, while the computational domain is fixed and needs no re-meshing during the simulations. However, the degree of geometrical details that the coarse mesh contains has an impact onto numerical results, a fact which will be investigated/ clarified in this thesis. The presented method is a finite element method, easy to be incorporated into standard CFD codes, for simulating particulate flow or, in general, flows with immersed time-(in)dependent and complicated shaped objects. The aim is to analyze and validate the penalty method and compare, qualitatively and quantitatively, with the already validated FBM regarding the aspects of accuracy of the solution, efficiency, robustness and behavior of the solvers. Different techniques to avoid the numerical difficulties that arise by using penalty method will be particularly described and analyzed. Advisors/Committee Members: Turek, Stefan (advisor), Blum, Heribert (referee).

Subjects/Keywords: FEM; Immersed boundary objects; Fictitious boundary method; Incompressible flows; Monolithic Newton multigrid; Penalty method; 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Anca, D. (2014). Fictitious boundary and penalization methods for treatment of rigid objects in incompressible flows. (Doctoral Dissertation). Technische Universität Dortmund. Retrieved from http://dx.doi.org/10.17877/DE290R-15342

Chicago Manual of Style (16^th Edition):

Anca, Dan. “Fictitious boundary and penalization methods for treatment of rigid objects in incompressible flows.” 2014. Doctoral Dissertation, Technische Universität Dortmund. Accessed April 12, 2021. http://dx.doi.org/10.17877/DE290R-15342.

MLA Handbook (7^th Edition):

Anca, Dan. “Fictitious boundary and penalization methods for treatment of rigid objects in incompressible flows.” 2014. Web. 12 Apr 2021.

Vancouver:

Anca D. Fictitious boundary and penalization methods for treatment of rigid objects in incompressible flows. [Internet] [Doctoral dissertation]. Technische Universität Dortmund; 2014. [cited 2021 Apr 12]. Available from: http://dx.doi.org/10.17877/DE290R-15342.

Council of Science Editors:

Anca D. Fictitious boundary and penalization methods for treatment of rigid objects in incompressible flows. [Doctoral Dissertation]. Technische Universität Dortmund; 2014. Available from: http://dx.doi.org/10.17877/DE290R-15342

University of Utah

27. Kordy, Michal Adam. Efficient computational methods for electromagnetic imaging with applications to 3D magnetotellurics.

Degree: PhD, Mathematics, 2014, University of Utah

URL: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3313/rec/835

► The motivation for this work is the forward and inverse problem for magnetotellurics, a frequency domain electromagnetic remote-sensing geophysical method used in mineral, geothermal, and… (more)

▼ The motivation for this work is the forward and inverse problem for magnetotellurics, a frequency domain electromagnetic remote-sensing geophysical method used in mineral, geothermal, and groundwater exploration. The dissertation consists of four papers. In the first paper, we prove the existence and uniqueness of a representation of any vector field in H(curl) by a vector lying in H(curl) and H(div). It allows us to represent electric or magnetic fields by another vector field, for which nodal finite element approximation may be used in the case of non-constant electromagneticproperties. With this approach, the system matrix does not become ill-posed for lowfrequency In the second paper, we consider hexahedral finite element approximation of an electric field for the magnetotelluric forward problem. The near-null space of the system matrix for low frequencies makes the numerical solution unstable in the air. We show that the proper solution may obtained by applying a correction on the nullspace of the curl. It is done by solving a Poisson equation using discrete Helmholtz decomposition. We parallelize the forward code on multicore workstation with large RAM. In the next paper, we use the forward code in the inversion. Regularization of the inversion is done by using the second norm of the logarithm of conductivity.The data space Gauss-Newton approach allows for significant savings in memory and computational time. We show the efficiency of the method by considering a numberof synthetic inversions and we apply it to real data collected in Cascade Mountains.The last paper considers a cross-frequency interpolation of the forward response as well as the Jacobian. We consider Pade approximation through model order reduction and rational Krylov subspace. The interpolating frequencies are chosen adaptively in order to minimize the maximum error of interpolation. Two error indicator functions are compared. We prove a theorem of almost always lucky failure in the case of the right hand analytically dependent on frequency. The operator's null space is treated by decomposing the solution into the part in the null space and orthogonal to it.

Subjects/Keywords: Finite element method; Inverse problem; Magnetotellurics; Maxwell's equations; Model order reduction; Rational krylov subspaces

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APA (6^th Edition):

Kordy, M. A. (2014). Efficient computational methods for electromagnetic imaging with applications to 3D magnetotellurics. (Doctoral Dissertation). University of Utah. Retrieved from http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3313/rec/835

Chicago Manual of Style (16^th Edition):

Kordy, Michal Adam. “Efficient computational methods for electromagnetic imaging with applications to 3D magnetotellurics.” 2014. Doctoral Dissertation, University of Utah. Accessed April 12, 2021. http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3313/rec/835.

MLA Handbook (7^th Edition):

Kordy, Michal Adam. “Efficient computational methods for electromagnetic imaging with applications to 3D magnetotellurics.” 2014. Web. 12 Apr 2021.

Vancouver:

Kordy MA. Efficient computational methods for electromagnetic imaging with applications to 3D magnetotellurics. [Internet] [Doctoral dissertation]. University of Utah; 2014. [cited 2021 Apr 12]. Available from: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3313/rec/835.

Council of Science Editors:

Kordy MA. Efficient computational methods for electromagnetic imaging with applications to 3D magnetotellurics. [Doctoral Dissertation]. University of Utah; 2014. Available from: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3313/rec/835

28. Lepilliez, Mathieu. Simulation numérique des ballotements d'ergols dans les réservoirs de satellites en microgravité et à faible nombre de Bond : Numerical modeling of sloshing of ergols in satellite tanks under microgravity conditions, and at low Bond numbers.

Degree: Docteur es, Dynamique des fluides, 2015, Université Toulouse III – Paul Sabatier

URL: http://www.theses.fr/2015TOU30248

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Cette thèse porte sur l'étude des ballotements dans les réservoirs de satellites à poste, lors des phases de manoeuvre à faible accélération. En effet la… (more)

Subjects/Keywords: Ecoulements diphasiques; Lignes triples; Frontières Immergées; Level-Set; Ghost Fluid Method; BlackBox Multigrid; Multiphase Flows; Contact lines; Immersed Interface Methods; Level-Set; Ghost Fluid Method; BlackBox Multigrid

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Lepilliez, M. (2015). Simulation numérique des ballotements d'ergols dans les réservoirs de satellites en microgravité et à faible nombre de Bond : Numerical modeling of sloshing of ergols in satellite tanks under microgravity conditions, and at low Bond numbers. (Doctoral Dissertation). Université Toulouse III – Paul Sabatier. Retrieved from http://www.theses.fr/2015TOU30248

Chicago Manual of Style (16^th Edition):

Lepilliez, Mathieu. “Simulation numérique des ballotements d'ergols dans les réservoirs de satellites en microgravité et à faible nombre de Bond : Numerical modeling of sloshing of ergols in satellite tanks under microgravity conditions, and at low Bond numbers.” 2015. Doctoral Dissertation, Université Toulouse III – Paul Sabatier. Accessed April 12, 2021. http://www.theses.fr/2015TOU30248.

MLA Handbook (7^th Edition):

Lepilliez, Mathieu. “Simulation numérique des ballotements d'ergols dans les réservoirs de satellites en microgravité et à faible nombre de Bond : Numerical modeling of sloshing of ergols in satellite tanks under microgravity conditions, and at low Bond numbers.” 2015. Web. 12 Apr 2021.

Vancouver:

Lepilliez M. Simulation numérique des ballotements d'ergols dans les réservoirs de satellites en microgravité et à faible nombre de Bond : Numerical modeling of sloshing of ergols in satellite tanks under microgravity conditions, and at low Bond numbers. [Internet] [Doctoral dissertation]. Université Toulouse III – Paul Sabatier; 2015. [cited 2021 Apr 12]. Available from: http://www.theses.fr/2015TOU30248.

Council of Science Editors:

Lepilliez M. Simulation numérique des ballotements d'ergols dans les réservoirs de satellites en microgravité et à faible nombre de Bond : Numerical modeling of sloshing of ergols in satellite tanks under microgravity conditions, and at low Bond numbers. [Doctoral Dissertation]. Université Toulouse III – Paul Sabatier; 2015. Available from: http://www.theses.fr/2015TOU30248

University of Manchester

29. Berljafa, Mario. Rational Krylov Decompositions: Theory and Applications.

Degree: 2017, University of Manchester

URL: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:306961

► Numerical methods based on rational Krylov spaces have become an indispensabletool of scientific computing. In this thesis we study rational Krylov spaces by consideringrational Krylov… (more)

▼ Numerical methods based on rational Krylov spaces have become an indispensabletool of scientific computing. In this thesis we study rational Krylov spaces by consideringrational Krylov decompositions; matrix relations which, under certain conditions,are associated with these spaces. We investigate the algebraic properties of suchdecompositions and present an implicit Q theorem for rational Krylov spaces.We derive standard and harmonic Ritz extraction strategies for approximatingthe eigenpairs of a matrix and for approximating the action of a matrix functiononto a vector. While these topics have been considered previously, our approachdoes not require the last pole to be infinite, which makes the extraction procedurecomputationally more efficient.Typically, the computationally most expensive component of the rational Arnoldialgorithm for computing a rational Krylov basis is the solution of a large linear systemof equations at each iteration. We explore the option of solving several linear systemssimultaneously, thus constructing the rational Krylov basis in parallel. If this is notdone carefully, the basis being orthogonalized may become poorly conditioned, leadingto numerical instabilities in the orthogonalization process. We introduce the newconcept of continuation pairs which gives rise to a near-optimal parallelization strategythat allows to control the growth of the condition number of this nonorthogonal basis.As a consequence we obtain a more accurate and reliable parallel rational Arnoldialgorithm. The computational benefits are illustrated using our high performance C++implementation.We develop an iterative algorithm for solving nonlinear rational least squaresproblems. The difficulty is in finding the poles of a rational function. For this purpose,at each iteration a rational Krylov decomposition is constructed and a modified linearproblem is solved in order to relocate the poles to new ones. Our numerical resultsindicate that the algorithm, called RKFIT, is well suited for model order reductionof linear time invariant dynamical systems and for optimisation problems related toexponential integration. Furthermore, we derive a strategy for the degree reduction ofthe approximant obtained by RKFIT. The rational function obtained by RKFIT isrepresented with the aid of a scalar rational Krylov decomposition and an additionalcoefficient vector. A function represented in this form is called an RKFUN. We developefficient methods for the evaluation, pole and root finding, and for performing basicarithmetic operations with RKFUNs.Lastly, we discuss RKToolbox, a rational Krylov toolbox for MATLAB, whichimplements all our algorithms and is freely available from http://rktoolbox.org.RKToolbox also features an extensive guide and a growing number of examples. Inparticular, most of our numerical experiments are easily reproducible by downloadingthe toolbox and running the corresponding example files in MATLAB. Advisors/Committee Members: GUETTEL, STEFAN SD, Tisseur, Francoise, Guettel, Stefan.

Subjects/Keywords: rational Krylov method; rational Arnoldi algorithm; rational Krylov space; Ritz values; harmonic Ritz values; matrix functions; parallelization; rational approximation; RKFIT; RKFUN; RKToolbox

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APA (6^th Edition):

Berljafa, M. (2017). Rational Krylov Decompositions: Theory and Applications. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:306961

Chicago Manual of Style (16^th Edition):

Berljafa, Mario. “Rational Krylov Decompositions: Theory and Applications.” 2017. Doctoral Dissertation, University of Manchester. Accessed April 12, 2021. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:306961.

MLA Handbook (7^th Edition):

Berljafa, Mario. “Rational Krylov Decompositions: Theory and Applications.” 2017. Web. 12 Apr 2021.

Vancouver:

Berljafa M. Rational Krylov Decompositions: Theory and Applications. [Internet] [Doctoral dissertation]. University of Manchester; 2017. [cited 2021 Apr 12]. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:306961.

Council of Science Editors:

Berljafa M. Rational Krylov Decompositions: Theory and Applications. [Doctoral Dissertation]. University of Manchester; 2017. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:306961

30. Rudimar Luiz Nós. \"Simulações de escoamentos tridimensionais bifásicos empregando métodos adaptativos e modelos de campo fase\".

Degree: 2007, University of São Paulo

URL: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-08052007-143200/

►

Este é o primeiro trabalho que apresenta simulações tridimensionais completamente adaptativas de um modelo de campo de fase para um fluido incompressível com densidade de… (more)

▼

Este é o primeiro trabalho que apresenta simulações tridimensionais completamente adaptativas de um modelo de campo de fase para um fluido incompressível com densidade de massa constante e viscosidade variável, conhecido como Modelo H. Solucionando numericamente as equações desse modelo em malhas refinadas localmente com a técnica AMR, simulamos computacionalmente escoamentos bifásicos tridimensionais. Os modelos de campo de fase oferecem uma aproximação física sistemática para investigar fenômenos que envolvem sistemas multifásicos complexos, tais como fluidos com camadas de mistura, a separação de fases sob forças de cisalhamento e a evolução de micro-estruturas durante processos de solidificação. Como as interfaces são substituídas por delgadas regiões de transição (interfaces difusivas), as simulações de campo de fase requerem muita resolução nessas regiões para capturar corretamente a física do problema em estudo. Porém essa não é uma tarefa fácil de ser executada numericamente. As equações que caracterizam o modelo de campo de fase contêm derivadas de ordem elevada e intrincados termos não lineares, o que exige uma estratégia numérica eficiente capaz de fornecer precisão tanto no tempo quanto no espaço, especialmente em três dimensões. Para obter a resolução exigida no tempo, usamos uma discretização semi-implícita de segunda ordem para solucionar as equações acopladas de Cahn-Hilliard e Navier-Stokes (Modelo H). Para resolver adequadamente as escalas físicas relevantes no espaço, utilizamos malhas refinadas localmente que se adaptam dinamicamente para recobrir as regiões de interesse do escoamento, como por exemplo, as vizinhanças das interfaces do fluido. Demonstramos a eficiência e a robustez de nossa metodologia com simulações que incluem a separação dos componentes de uma mistura bifásica, a deformação de gotas sob cisalhamento e as instabilidades de Kelvin-Helmholtz.

This is the first work that introduces 3D fully adaptive simulations for a phase field model of an incompressible fluid with matched densities and variable viscosity, known as Model H. Solving numerically the equations of this model in meshes locally refined with AMR technique, we simulate computationally tridimensional two-phase flows. Phase field models offer a systematic physical approach to investigate complex multiphase systems phenomena such as fluid mixing layers, phase separation under shear and microstructure evolution during solidification processes. As interfaces are replaced by thin transition regions (diffuse interfaces), phase field simulations need great resolution in these regions to capture correctly the physics of the studied problem. However, this is not an easy task to do numerically. Phase field model equations…

Advisors/Committee Members: Alexandre Megiorin Roma, Héctor Daniel Ceniceros, Héctor Daniel Ceniceros, Admilson Teixeira Franco, Julio Romano Meneghini, Leandro Franco de Souza.

Subjects/Keywords: equação biharmônica; método adaptativo; métodos semi-implícitos; modelos de campo de fase conservativos; multinível-multigrid; refinamento de malhas adaptativas; separação dos componentes de uma mistura bifásica; adaptive mesh refinement; adaptive method; biharmonic equation; conservative phase field models; multilevel multigrid; semi-implicit methods; spinodal decomposition

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Nós, R. L. (2007). \"Simulações de escoamentos tridimensionais bifásicos empregando métodos adaptativos e modelos de campo fase\". (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/45/45132/tde-08052007-143200/

Chicago Manual of Style (16^th Edition):

Nós, Rudimar Luiz. “\"Simulações de escoamentos tridimensionais bifásicos empregando métodos adaptativos e modelos de campo fase\".” 2007. Doctoral Dissertation, University of São Paulo. Accessed April 12, 2021. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-08052007-143200/.

MLA Handbook (7^th Edition):

Nós, Rudimar Luiz. “\"Simulações de escoamentos tridimensionais bifásicos empregando métodos adaptativos e modelos de campo fase\".” 2007. Web. 12 Apr 2021.

Vancouver:

Nós RL. \"Simulações de escoamentos tridimensionais bifásicos empregando métodos adaptativos e modelos de campo fase\". [Internet] [Doctoral dissertation]. University of São Paulo; 2007. [cited 2021 Apr 12]. Available from: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-08052007-143200/.

Council of Science Editors:

Nós RL. \"Simulações de escoamentos tridimensionais bifásicos empregando métodos adaptativos e modelos de campo fase\". [Doctoral Dissertation]. University of São Paulo; 2007. Available from: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-08052007-143200/

Open Access Theses and Dissertations