Search Results for multigrid-methods-for-finite-elements

Multigrid Methods for Finite Elements combines two rapidly developing fields: finite element methods, and multigrid algorithms.

Author: V.V. Shaidurov

Publisher: Springer Science & Business Media

ISBN: 9789401585279

Category: Mathematics

Page: 334

View: 719

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Multigrid Methods for Finite Elements combines two rapidly developing fields: finite element methods, and multigrid algorithms. At the theoretical level, Shaidurov justifies the rate of convergence of various multigrid algorithms for self-adjoint and non-self-adjoint problems, positive definite and indefinite problems, and singular and spectral problems. At the practical level these statements are carried over to detailed, concrete problems, including economical constructions of triangulations and effective work with curvilinear boundaries, quasilinear equations and systems. Great attention is given to mixed formulations of finite element methods, which allow the simplification of the approximation of the biharmonic equation, the steady-state Stokes, and Navier--Stokes problems.
2013-03-09 By V.V. Shaidurov

This is the first comprehensive monograph that features state-of-the-art multigrid methods for enhancing the modeling versatility, numerical robustness, and computational efficiency of one of the most popular classes of numerical ...

Author: Yu Zhu

Publisher: John Wiley & Sons

ISBN: 9780471786375

Category: Science

Page: 440

View: 451

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This is the first comprehensive monograph that featuresstate-of-the-art multigrid methods for enhancing the modelingversatility, numerical robustness, and computational efficiency ofone of the most popular classes of numerical electromagnetic fieldmodeling methods: the method of finite elements. The focus of thepublication is the development of robust preconditioners for theiterative solution of electromagnetic field boundary value problems(BVPs) discretized by means of finite methods. Specifically, the authors set forth their own successful attemptsto utilize concepts from multigrid and multilevel methods for theeffective preconditioning of matrices resulting from theapproximation of electromagnetic BVPs using finite methods.Following the authors' careful explanations and step-by-stepinstruction, readers can duplicate the authors' results and takeadvantage of today's state-of-the-art multigrid/multilevelpreconditioners for finite element-based iterative electromagneticfield solvers. Among the highlights of coverage are: * Application of multigrid, multilevel, and hybridmultigrid/multilevel preconditioners to electromagnetic scatteringand radiation problems * Broadband, robust numerical modeling of passive microwavecomponents and circuits * Robust, finite element-based modal analysis of electromagneticwaveguides and cavities * Application of Krylov subspace-based methodologies forreduced-order macromodeling of electromagnetic devices andsystems * Finite element modeling of electromagnetic waves in periodicstructures The authors provide more than thirty detailed algorithms alongsidepseudo-codes to assist readers with practical computerimplementation. In addition, each chapter includes an applicationssection with helpful numerical examples that validate the authors'methodologies and demonstrate their computational efficiency androbustness. This groundbreaking book, with its coverage of an exciting newenabling computer-aided design technology, is an essentialreference for computer programmers, designers, and engineers, aswell as graduate students in engineering and applied physics.
2006-03-10 By Yu Zhu

of the error can be accurately captured on the coarser grid.

Author: Susanne C. Brenner

Publisher:

ISBN: OCLC:68299693

Category:

Page: 95

View: 796

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of the error can be accurately captured on the coarser grid. Furthermore, since the error correction is done on a coarser grid, less compuational work is involved. The multigrid method is optimal in the sense that the cost of computation is proportional to the number of unknowns.

Author: Wang Ming

Publisher:

ISBN: OCLC:897935196

Category:

Page: 13

View: 532

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1991 By Wang Ming

Author: James Bramble

Publisher:

ISBN: CORNELL:31924072744661

Category:

Page: 22

View: 559

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1994 By James Bramble

Author: J. Molenaar

Publisher:

ISBN: STANFORD:36105009148276

Category: Mathematics

Page: 134

View: 480

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1993 By J. Molenaar

Author: Stefan Reitzinger

Publisher:

ISBN: 3854872593

Category: matematika - numerična analiza - numerične metode - mrežne metode - eliptične diferencialne enačbe - linearni prostori - disertacije

Page: 117

View: 637

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INTRODUCTION Recently, there has been some attempt to prove convergence estimates for nonconforming multigrid methods for partial differential problems with less than full elliptic regularity [17, 45]. Since nonconforming finite element ...

Author:

Publisher:

ISBN:

Category:

Page: 172

View: 605

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1998 By

All relevant implementation aspects of finite element methods are discussed in this book.

Author: Martin Weiser

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110386189

Category: Mathematics

Page: 157

View: 585

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All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered only as far as it gives insight into the construction of algorithms. In the exercises, a complete FE-solver for stationary 2D problems is implemented in Matlab/Octave. Contents: Finite Element Fundamentals Grids and Finite Elements Assembly Solvers Error Estimation Mesh Refinement Multigrid Elastomechanics Fluid Mechanics Grid Data Structure Function Reference
2016-05-10 By Martin Weiser

The test cases considered are complicated to solve and the numerical results show the robustness and efficiency of the new preconditioners.

Author: Ali Aghabarati

Publisher:

ISBN: OCLC:880373142

Category:

Page:

View: 128

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The test cases considered are complicated to solve and the numerical results show the robustness and efficiency of the new preconditioners. Deflated Krylov methods preconditioned with the current Multilevel/ASP/AMG approach are always considerably faster than the reference methods and speedups of up to 10 are achieved for some test problems. " --
2014 By Ali Aghabarati