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.
Inhaltsverzeichnis
List of Figures.
List of Tables.
Preface.
Acknowledgments.
1. Introduction.
2. Hierarchical Basis Functions for Triangles and
Tetrahedra.
3. Finite Element Formulations of Electromagnetic BVPs.
4. Iterative Methods, Preconditioners, and Multigrid.
5. Nested Multigrid Preconditioner.
6. Nested Multigrid Vector and Scaler Potential
Preconditioner.
7. Hierarchical Multilevel and Hybrid Potential
Preconditioners.
8. Krylov-Subspace Based Eigenvalue Analysis.
9. Two-Dimensional Eigenvalue Analysis of Waveguides.
10. Three-Dimensional Eigenvalue Analysis of Resonators.
11. Model Order Reduction of Electromagnetic Systems.
12. Finite Element Analysis of Periodic Structures.
Appendix A: Identities and Theorems from Vector Calculus.
Index.
Über den Autor
Dr.Yu Zhu has been a member of the consulting staff in
Custom IC at Cadence Design Systems, Inc. since 2002. He
earned his B.S. in Electrical Engineering at Nanjing University in
1995, his M.S. at Ohio State University in 1998, and his Ph.D. at
University of Illinois @ Urbana-Champaign in 2002. He is a
member of the IEEE and Sigma Xi.
Dr. Andreas Cangellaris has been a full professor at
University of Illinois @ Urbana-Champaign since 1997. His
research work has been in the area of applied and computational
electromagnetics with emphasis on thier application to electrical
modeling simulation of RF/microwave components and systems,
high-speed digital interconnects at the board, package, and chip
level, as well as the modeling and simulation of electromagnetic
compatibility and electromagnetic interference. He has
co-authored more than 150 refereed papers and three book chapters
on topics related to computational electromagnetics and
interconnects and package modeling and simulation. He was
elected a Fellow of the IEEE in January 2000.
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