Multigrid Finite Element Methods for Electromagnetic Field Modeling

Yu Zhu, Andreas Cangellaris - Collection IEEE Press Series on Electromagnetic Wave Theory

410 pages, parution le 20/03/2006

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Résumé

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 electromagnetic field modeling methods: the method of finite elements. The focus of the publication is the development of robust preconditioners for the iterative solution of electromagnetic field boundary value problems (BVPs) discretized by means of finite methods.

Specifically, the authors set forth their own successful attempts to utilize concepts from multigrid and multilevel methods for the effective preconditioning of matrices resulting from the approximation of electromagnetic BVPs using finite methods. Following the authors' careful explanations and step-by-step instruction, readers can duplicate the authors' results and take advantage of today's state-of-the-art multigrid/multilevel preconditioners for finite element-based iterative electromagnetic field solvers.

Among the highlights of coverage are:

Application of multigrid, multilevel, and hybrid multigrid/multilevel preconditioners to electromagnetic scattering and radiation problems
Broadband, robust numerical modeling of passive microwave components and circuits
Robust, finite element-based modal analysis of electromagnetic waveguides and cavities
Application of Krylov subspace-based methodologies for reduced-order macromodeling of electromagnetic devices and systems
Finite element modeling of electromagnetic waves in periodic structures

The authors provide more than thirty detailed algorithms alongside pseudo-codes to assist readers with practical computer implementation. In addition, each chapter includes an applications section with helpful numerical examples that validate the authors' methodologies and demonstrate their computational efficiency and robustness.

This groundbreaking book, with its coverage of an exciting new enabling computer-aided design technology, is an essential reference for computer programmers, designers, and engineers, as well as graduate students in engineering and applied physics.

Sommaire

Introduction
Hierarchical Basis Functions for Triangles and Tetrahedra
Finite Element Formulations of Electromagnetic BVPs
Iterative Methods, Preconditioners, and Multigrid
Nested Multigrid Preconditioner
Nested Multigrid Vector and Scaler Potential Preconditioner
Hierarchical Multilevel and Hybrid Potential Preconditioners
Krylov-Subspace Based Eigenvalue Analysis
Two-Dimensional Eigenvalue Analysis of Waveguides
Three-Dimensional Eigenvalue Analysis of Resonators
Model Order Reduction of Electromagnetic Systems
Finite Element Analysis of Periodic Structures
Appendix A: Identities and Theorems from Vector Calculus

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	Yu Zhu, Andreas Cangellaris
Collection	IEEE Press Series on Electromagnetic Wave Theory
Parution	20/03/2006
Nb. de pages	410
Format	18 x 26
Couverture	Relié
Poids	880g
Intérieur	Noir et Blanc
EAN13	9780471741107
ISBN13	978-0-471-74110-7