Yu Zhu

Andreas C. Cangellaris

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.

Multigrid Finite Element Methods for Electromagnetic Field Modeling

Lei Liu

Computational nanoelectronics is an emerging multi-disciplinary field covering condensed matter physics, applied mathematics, computer science, and electronic engineering. In recent decades, a few state-of-the-art software packages have been developed to carry out first-principle atomistic device simulations. Nevertheless those packages are either black boxes (commercial codes) or accessible only to very limited users (private research codes). The purpose of this book is to open one of the commercial black boxes, and to demonstrate the complete procedure from theoretical derivation, to numerical implementation, all the way to device simulation. Meanwhile the affiliated source code constitutes an open platform for new researchers. This is the first book of its kind. We hope the book will make a modest contribution to the field of computational nanoelectronics. Contents:IntroductionThe NECPA TheoryThe NECPA-LMTO MethodNanoDsim: The Package DesignNanoDsim: Bulk SystemsNanoDsim: Two-Probe SystemsNanoDsim: Optimization and ParallelizationKaleidoscope of the Physics in Disordered SystemsAppendix Readership: Post-graduate students or professional researchers who are interested in computational physics, device physics, quantum transport, disorder systems, and overlap of the above.

Yu Zhu

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