subject:(deflation 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 11, 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. 11 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 11]. 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. Sangers, A. (author). Enhancing iterative solution methods for general FEM computations using rigid body modes.

Degree: 2014, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:8c564409-ed5a-4ca5-b55f-b85e16814076

Applied Mathematics

Numerical Analysis

Electrical Engineering, Mathematics and Computer Science

Advisors/Committee Members: Van Gijzen, M.B. (mentor), Vuik, C. (mentor), Schreppers, G.M.A. (mentor), Dubbeldam, J.L.A. (mentor).

Subjects/Keywords: Rigid body modes; Approximate rigid body; Deflation; Coarse grid correction; FEM; Finite elements; Iterative solution method

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APA (6^th Edition):

Sangers, A. (. (2014). Enhancing iterative solution methods for general FEM computations using rigid body modes. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:8c564409-ed5a-4ca5-b55f-b85e16814076

Chicago Manual of Style (16^th Edition):

Sangers, A (author). “Enhancing iterative solution methods for general FEM computations using rigid body modes.” 2014. Masters Thesis, Delft University of Technology. Accessed April 11, 2021. http://resolver.tudelft.nl/uuid:8c564409-ed5a-4ca5-b55f-b85e16814076.

MLA Handbook (7^th Edition):

Sangers, A (author). “Enhancing iterative solution methods for general FEM computations using rigid body modes.” 2014. Web. 11 Apr 2021.

Vancouver:

Sangers A(. Enhancing iterative solution methods for general FEM computations using rigid body modes. [Internet] [Masters thesis]. Delft University of Technology; 2014. [cited 2021 Apr 11]. Available from: http://resolver.tudelft.nl/uuid:8c564409-ed5a-4ca5-b55f-b85e16814076.

Council of Science Editors:

Sangers A(. Enhancing iterative solution methods for general FEM computations using rigid body modes. [Masters Thesis]. Delft University of Technology; 2014. Available from: http://resolver.tudelft.nl/uuid:8c564409-ed5a-4ca5-b55f-b85e16814076

3. Malandain, Mathias. Simulations massivement parallèles des écoulements turbulents à faible nombre de Mach : Massively parallel simulation of low-Mach number turbulent flow.

Degree: Docteur es, Sciences pour l'ingénieur, 2013, Rouen, INSA

URL: http://www.theses.fr/2013ISAM0006

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L'objectif de cette thèse est l'accélération des solveurs de Gradient Conjugué avec déflation utilisés pour la résolution de l'équation de Poisson pour la pression, dans… (more)

Subjects/Keywords: Mécanique des fluides numériques; Gradients conjugués; Méthode de déflation; Analyse numérique; Méthodes multiniveaux; Conjugate gradient; Low-Mach number; Turbulents flows; Digital fluid mechanics; Deflation method

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

APA (6^th Edition):

Malandain, M. (2013). Simulations massivement parallèles des écoulements turbulents à faible nombre de Mach : Massively parallel simulation of low-Mach number turbulent flow. (Doctoral Dissertation). Rouen, INSA. Retrieved from http://www.theses.fr/2013ISAM0006

Chicago Manual of Style (16^th Edition):

Malandain, Mathias. “Simulations massivement parallèles des écoulements turbulents à faible nombre de Mach : Massively parallel simulation of low-Mach number turbulent flow.” 2013. Doctoral Dissertation, Rouen, INSA. Accessed April 11, 2021. http://www.theses.fr/2013ISAM0006.

MLA Handbook (7^th Edition):

Malandain, Mathias. “Simulations massivement parallèles des écoulements turbulents à faible nombre de Mach : Massively parallel simulation of low-Mach number turbulent flow.” 2013. Web. 11 Apr 2021.

Vancouver:

Malandain M. Simulations massivement parallèles des écoulements turbulents à faible nombre de Mach : Massively parallel simulation of low-Mach number turbulent flow. [Internet] [Doctoral dissertation]. Rouen, INSA; 2013. [cited 2021 Apr 11]. Available from: http://www.theses.fr/2013ISAM0006.

Council of Science Editors:

Malandain M. Simulations massivement parallèles des écoulements turbulents à faible nombre de Mach : Massively parallel simulation of low-Mach number turbulent flow. [Doctoral Dissertation]. Rouen, INSA; 2013. Available from: http://www.theses.fr/2013ISAM0006

Delft University of Technology

4. 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 11, 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. 11 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 11]. 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

5. Porter, Andrew. Pooling Methods and Similarity Measures for Fractional Factorial Designs in the Presence of an Auxiliary Variable.

Degree: MS, Department of Mathematics and Statistics, 2017, University of Guelph

URL: https://atrium.lib.uoguelph.ca/xmlui/handle/10214/10444

► It is well-known that the standard mean squared error obtained from a half fractional factorial provides a conservative estimate of the error variance, which can… (more)

Subjects/Keywords: Fractional Factorial Designs; Error Pooling Methods; Auxiliary Variable; Deflation Method; Adjusted Method

…2.2.2 Deflation Method The next alternative pooling structure to be analyzed will be referred… …to as the deflation method. This process requires the researcher to first calculate a… …unadjusted method for the fractional factorial design. The notation for the Deflation statistic is… …statistic. The main potential drawback of this method will be an over deflation of the MSE in the… …methods for each of the response variables in the real data sets. The deflation method has good…

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

APA (6^th Edition):

Porter, A. (2017). Pooling Methods and Similarity Measures for Fractional Factorial Designs in the Presence of an Auxiliary Variable. (Masters Thesis). University of Guelph. Retrieved from https://atrium.lib.uoguelph.ca/xmlui/handle/10214/10444

Chicago Manual of Style (16^th Edition):

Porter, Andrew. “Pooling Methods and Similarity Measures for Fractional Factorial Designs in the Presence of an Auxiliary Variable.” 2017. Masters Thesis, University of Guelph. Accessed April 11, 2021. https://atrium.lib.uoguelph.ca/xmlui/handle/10214/10444.

MLA Handbook (7^th Edition):

Porter, Andrew. “Pooling Methods and Similarity Measures for Fractional Factorial Designs in the Presence of an Auxiliary Variable.” 2017. Web. 11 Apr 2021.

Vancouver:

Porter A. Pooling Methods and Similarity Measures for Fractional Factorial Designs in the Presence of an Auxiliary Variable. [Internet] [Masters thesis]. University of Guelph; 2017. [cited 2021 Apr 11]. Available from: https://atrium.lib.uoguelph.ca/xmlui/handle/10214/10444.

Council of Science Editors:

Porter A. Pooling Methods and Similarity Measures for Fractional Factorial Designs in the Presence of an Auxiliary Variable. [Masters Thesis]. University of Guelph; 2017. Available from: https://atrium.lib.uoguelph.ca/xmlui/handle/10214/10444

6. Kaliszka, K.B. (author). Developing a parallel solver mechanical problems.

Degree: 2010, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:cea77d32-d6df-443c-9cee-ca89e21733ac

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In this master thesis I investigate the case of solving linear systems which correspond to mechanical problems with the use of Deflated Preconditioned Conjugate Method… (more)

Subjects/Keywords: Domain Decompostion; Additive Schwarz Method; Deflation; Precondtioned Conjugate Gradient; Deflated Precondtioned Conjugate Gradient; Region Growth Algorithm

…solution for our problem. This chapter is followed by a description of the Deflation method and… …systems of the subdomains, and the Deflation method to improve the spread of the information… …introduction to the Finite Element Method, which is done in the next chapter. After that, we are… …x28;1.8) The Eq. (1.8) is then solved with the use of Finite Element Method… …Finite Element Method 2.1 Introduction When dealing with partial differential equations, we…

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

APA (6^th Edition):

Kaliszka, K. B. (. (2010). Developing a parallel solver mechanical problems. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:cea77d32-d6df-443c-9cee-ca89e21733ac

Chicago Manual of Style (16^th Edition):

Kaliszka, K B (author). “Developing a parallel solver mechanical problems.” 2010. Masters Thesis, Delft University of Technology. Accessed April 11, 2021. http://resolver.tudelft.nl/uuid:cea77d32-d6df-443c-9cee-ca89e21733ac.

MLA Handbook (7^th Edition):

Kaliszka, K B (author). “Developing a parallel solver mechanical problems.” 2010. Web. 11 Apr 2021.

Vancouver:

Kaliszka KB(. Developing a parallel solver mechanical problems. [Internet] [Masters thesis]. Delft University of Technology; 2010. [cited 2021 Apr 11]. Available from: http://resolver.tudelft.nl/uuid:cea77d32-d6df-443c-9cee-ca89e21733ac.

Council of Science Editors:

Kaliszka KB(. Developing a parallel solver mechanical problems. [Masters Thesis]. Delft University of Technology; 2010. Available from: http://resolver.tudelft.nl/uuid:cea77d32-d6df-443c-9cee-ca89e21733ac

Delft University of Technology

7. Tang, J.M. Two-level preconditioned conjugate gradient methods with applications to bubbly flow problems.

Degree: 2008, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; urn:NBN:nl:ui:24-uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; urn:NBN:nl:ui:24-uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; http://resolver.tudelft.nl/uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0

► The Preconditioned Conjugate Gradient (PCG) method is one of the most popular iterative methods for solving large linear systems with a symmetric and positive semi-definite… (more)

Subjects/Keywords: conjugate gradient method; two-level preconditioners; deflation; domain decomposition; multigrid; bubbly flows; poisson equation with a discontinuous coefficient; singular symmetric positive semi-definite matrices

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

APA (6^th Edition):

Tang, J. M. (2008). Two-level preconditioned conjugate gradient methods with applications to bubbly flow problems. (Doctoral Dissertation). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; urn:NBN:nl:ui:24-uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; urn:NBN:nl:ui:24-uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; http://resolver.tudelft.nl/uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0

Chicago Manual of Style (16^th Edition):

Tang, J M. “Two-level preconditioned conjugate gradient methods with applications to bubbly flow problems.” 2008. Doctoral Dissertation, Delft University of Technology. Accessed April 11, 2021. http://resolver.tudelft.nl/uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; urn:NBN:nl:ui:24-uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; urn:NBN:nl:ui:24-uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; http://resolver.tudelft.nl/uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0.

MLA Handbook (7^th Edition):

Tang, J M. “Two-level preconditioned conjugate gradient methods with applications to bubbly flow problems.” 2008. Web. 11 Apr 2021.

Vancouver:

Tang JM. Two-level preconditioned conjugate gradient methods with applications to bubbly flow problems. [Internet] [Doctoral dissertation]. Delft University of Technology; 2008. [cited 2021 Apr 11]. Available from: http://resolver.tudelft.nl/uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; urn:NBN:nl:ui:24-uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; urn:NBN:nl:ui:24-uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; http://resolver.tudelft.nl/uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0.

Council of Science Editors:

Tang JM. Two-level preconditioned conjugate gradient methods with applications to bubbly flow problems. [Doctoral Dissertation]. Delft University of Technology; 2008. Available from: http://resolver.tudelft.nl/uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; urn:NBN:nl:ui:24-uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; urn:NBN:nl:ui:24-uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0 ; http://resolver.tudelft.nl/uuid:e8c5f63b-ee7d-4a59-90da-a8025f5f88b0

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