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1. 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 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 (6th 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 (16th 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 13, 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 (7th Edition):

Wobker, Hilmar. “Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems.” 2010. Web. 13 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 13]. 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

2. 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, 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 (6th 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 (16th 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 13, 2021. http://dx.doi.org/10.17877/DE290R-497.

MLA Handbook (7th Edition):

Wobker, Hilmar. “Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems.” 2010. Web. 13 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 13]. 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

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