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Computational Electromagnetics
Domain Decomposition Methods and Practical Applications



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ISBN 9781466510494
December 31, 2021 Forthcoming by CRC Press
512 Pages 50 Color & 167 B/W Illustrations

 
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Book Description

Developed for Computational Physicists, Researchers, and Software Developers at the Practical Level

Integrating in-depth mathematical analysis with real-world engineering practice, Computational Electromagnetics: Domain Decomposition Methods and Practical Applications focuses on domain decomposition methods (DDMs) that adequately deal with the vector wave equation. Dedicated specifically to solving time harmonic Maxwell equations, it covers challenges that are typically hard to address using conventional numerical methods. This book adopts the philosophy throughout, that every residual will either equal identically to zero through restrictions on the trial functions or be tested by test functions by ways of dual-pairing.

Explore the Use of DDM to Solve Large-Scale Problems

The material focuses on a multi-trace combined field integral equation formulation with multiple traces derived and analyzed for EM scattering from a single homogeneous scatter, and contains numerical examples demonstrating the benefits (accuracy and scalability) of DDM. It provides examples for analyzing and addressing scattering problems that include an electromagnetic wave scattering from a large complex large-scale composite mockup aircraft and an electromagnetic wave scattering from an electrically large inlet structure. Presenting numerous facets of the nonoverlapping domain decomposition methods and their applications, it reveals how these methods can help solve multi-scale time harmonic electromagnetic problems.

This book covers:

  • Large finite antenna arrays, metamaterials, antenna systems conformally mounted on large platforms, signal integrity analyses of complex integrated circuits and packaging, and radar echo area computation of complex composite targets applications
  • An alternative approach to formulate the corresponding boundary value problem by incorporating an additional vector variable defined only on the surface
  • The multi-solver domain decomposition method (MS-DDM) which is included in theory and practical engineering applications

Computational Electromagnetics: Domain Decomposition Methods and Practical Applications covers the applied aspects of domain decomposition methods for computational electromagnetics, and helps to bridge the gap between multi-scale and multi-physics, and the hands-on application of practical engineering.

Table of Contents

Overview of Maxwell Equations

Finite Element Formulation using Interior Penalty Approach

Conformal IP-DDM

Conformal DDM with Higher Order Transmission Conditions

Non-Conformal Finite Element Domain Decomposition for Electromagnetic Problems with Repetitions

2nd Order Transmission Conditions, Corner Edge Penalty and Global Preconditioner for Finite Element-Based Domain Decomposition Methods

Optimized Transmission Conditions for the Time-Harmonic Curl-Curl Maxwell's Equations

Non-conformal Domain Decomposition Methods for Power Integrity and Signal Integrity Analyses of Complex ICs and Packaging

Surface Integral Equations and IE-DDM

Multi-Trace Surface Integral Equation Methods for Penetrable Targets

Electromagnetic Scattering Analysis of a Large and Deep Inlet Embedded in an Arbitrarily Shaped Host Body

Hybrid Finite/Boundary Elements Method for Periodic Structures on Non-Periodic Meshes

Hybrid Finite Elements and Boundary Elements Methods

Multi-Solver DDM for Well Separated Regions

Non-Conformal DDMs for Solving Electrically Large Multi-Scale Electromagnetic Scattering Problems

Integral Equation Discontinuous Galerkin Method for EM Scattering from Non-Penetrable Targets

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Reviews

"… excellent coverage, by leaders in the field. The book should be useful to students and advanced researchers alike. Appropriate balance of depth and breadth. Nice demonstration of the place and relevance of Domain Decomposition Methods with respect to more traditional methods of Computational Electromagnetics on one side and state-of-the-art engineering Practical Applications on the other."
—Branislav M. Notaros, Colorado State University