Multigrid Methods for Finite Elements

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

ISBN: UOM:39015034226889

Category: Computers

Page: 360

View: 471

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.
Categories: Computers

Multigrid Methods for Finite Elements

Multigrid Methods for Finite Elements

[59] Girault V., Raviant P.A. Finite Element Methods for Navier-Stokes Equations. – Springer: Berlin, N. Y., 1987. [60 Glowinski R., Marocco A. Analyse numerique du champ magnetique d'un alternateur par elements finis et sur-relaxation ...

Author: V.V. Shaidurov

Publisher: Springer Science & Business Media

ISBN: 9789401585279

Category: Mathematics

Page: 334

View: 665

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.
Categories: Mathematics

Multigrid Finite Element Methods for Electromagnetic Field Modeling

Multigrid Finite Element Methods for Electromagnetic Field Modeling

us motivate some of the methodologies presented in this chapter toward the development of robust iterative finite element matrix solvers. The primary reason for the slow convergence of the iterative solution of electromagnetic finite ...

Author: Yu Zhu

Publisher: John Wiley & Sons

ISBN: 9780471786375

Category: Science

Page: 440

View: 966

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.
Categories: Science

Computation and Applied Mathematics

Computation and Applied Mathematics

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 ...

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Category:

Page: 172

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Seventh Copper Mountain Conference on Multigrid Methods

Seventh Copper Mountain Conference on Multigrid Methods

[ 2 ] R. E. BANK AND T.DUPONT , An optimal order process for solving finite element equations , Math . Comp . , 36 ( 1980 ) , pp . 35-51 . [ 3 ] D. BRAESS And R. Verfürth , Multigrid methods for nonconforming finite element methods ...

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Publisher:

ISBN: NASA:31769000471683

Category:

Page: 438

View: 650

Categories:

Multigrid Methods

Multigrid Methods

108. techniques for mixed finite element methods with rectangular Raviart-Thomas elements, in “Domain Decomposition Methods,” T.F. Chan, R. Glowinski, J. Periaux, and O.B. Widlund, eds., SIAM, Philadelphi, Penn., 1989, pp. 98– 114.

Author: James H Bramble

Publisher: Routledge

ISBN: 9781351429856

Category: Mathematics

Page: 114

View: 952

Multigrid methods are among the most efficient iterative methods for the solution of linear systems which arise in many large scale scientific calculations. Every researcher working with the numerical solution of partial differential equations should at least be familiar with this powerful technique. This invaluable book presents results concerning the rates of convergence of multigrid iterations.
Categories: Mathematics

Proceedings of the Fourth Copper Mountain Conference on Multigrid Methods

Proceedings of the Fourth Copper Mountain Conference on Multigrid Methods

REFERENCES [ 1 ] D. Arnold and F. Brezzi , Mixed and nonconforming finite element methods : im- plementation , postprocessing and ... [ 6 ] S.C. Brenner , An optimal order multigrid method for P1 nonconforming finite elements , Math .

Author: Jan Mandel

Publisher: SIAM

ISBN: 0898712483

Category: Mathematics

Page: 462

View: 581

Categories: Mathematics

multigrid methods

multigrid methods

362 A Finite Element Method for the Euler Equations 24-28 1986 ) , to be published by computational Mechanics Pub . , Southampton ( UK ) [ 5 ] LOHNER R. , MORGAN K. , Unstructured Multigrid methods , Second European Conference on ...

Author: Stephen F. Mccormick

Publisher: CRC Press

ISBN: 9781000147223

Category: Mathematics

Page: 668

View: 767

This book is a collection of research papers on a wide variety of multigrid topics, including applications, computation and theory. It represents proceedings of the Third Copper Mountain Conference on Multigrid Methods, which was held at Copper Mountain, Colorado.
Categories: Mathematics

Multigrid Methods III

Multigrid Methods III

Arnold, D.N. and Brezzi, F., Mixed and nonconforming finite element methods, postprocessing and error estimates, M*AN 19 (1985), 7-32. . Braess, D. and Verfürth, R., Multi-grid methods for non-conforming finite element methods, ...

Author: HACKBUSCH

Publisher: Birkhäuser

ISBN: 9783034857123

Category: Science

Page: 394

View: 409

These proceedings contain a selection of papers presented at the Third European Conference on Multigrid Methods which was held in Bonn on October 1-4, 1990. Following conferences in 1981 and 1985, a platform for the presentation of new Multigrid results was provided for a third time. Multigrid methods no longer have problems being accepted by numerical analysts and users of numerical methods; on the contrary, they have been further developed in such a successful way that they have penetrated a variety of new fields of application. The high number of 154 participants from 18 countries and 76 presented papers show the need to continue the series of the European Multigrid Conferences. The papers of this volume give a survey on the current Multigrid situation; in particular, they correspond to those fields where new developments can be observed. For example, se veral papers study the appropriate treatment of time dependent problems. Improvements can also be noticed in the Multigrid approach for semiconductor equations. The field of parallel Multigrid variants, having been started at the second European Multigrid Conference, is now at the centre of interest.
Categories: Science

Multigrid Methods II

Multigrid Methods II

[3] BRANDT, A., Multigrid Techniques : 1984 Guide with Applications to Fluid Dynamics. G.M.D. - Studien Nr. 85, St. Augustin, l084. [4] BREZZI, F. and J. PITKARANTA, On the stabilization of finite element approximations of the Stokes ...

Author: Wolfgang Hackbusch

Publisher: Springer

ISBN: 9783540473725

Category: Mathematics

Page: 336

View: 927

Categories: Mathematics