Journal ArticleDOI
Computational electromagnetics: the physics of smooth versus oscillatory fields.
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TLDR
The paper elucidates the fact that the difference in the physics between solutions to Laplace's equation (static) and Maxwell's equations for dynamic problems (Helmholtz equation) affect the use of Laplacian field and Helmholtz field in imaging and the design of fast computational algorithms for electromagnetic scattering problems.Abstract:
This paper starts by discussing the difference in the physics between solutions to Laplace's equation (static) and Maxwell's equations for dynamic problems (Helmholtz equation). Their differing physical characters are illustrated by how the two fields convey information away from their source point. The paper elucidates the fact that their differing physical characters affect the use of Laplacian field and Helmholtz field in imaging. They also affect the design of fast computational algorithms for electromagnetic scattering problems. Specifically, a comparison is made between fast algorithms developed using wavelets, the simple fast multipole method, and the multi-level fast multipole algorithm for electrodynamics. The impact of the physical characters of the dynamic field on the parallelization of the multi-level fast multipole algorithm is also discussed. The relationship of diagonalization of translators to group theory is presented. Finally, future areas of research for computational electromagnetics are described.read more
Citations
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Recent Advances and Emerging Applications of the Boundary Element Method
Yijun Liu,Subrata Mukherjee,Naoshi Nishimura,Martin Schanz,Wenjing Ye,Alok Sutradhar,Ernian Pan,Ney Augusto Dumont,Attilio Frangi,Andrés Sáez +9 more
TL;DR: The paper aims to review the major research achievements in the last decade, the current status, and the future directions of the BEM in the next decade.
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A mixed-form fast multipole algorithm
Li Jun Jiang,Weng Cho Chew +1 more
TL;DR: A mixed-form fast multipole algorithm (MF-FMA) is proposed that has no low frequency break down, and it can work seamlessly from static to dynamic and from circuit physics to dynamic (where wave physics is important).
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A high order hybrid finite element method applied to the solution of electromagnetic wave scattering problems in the time domain
TL;DR: The development of a hybrid high order time domain finite element solution procedure for the simulation of two dimensional problems in computational electromagnetics is considered and an exact analytical solution is employed initially to validate the procedure and the numerical performance is then demonstrated for a number of more challenging examples.
References
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Principles of Optics
TL;DR: In this paper, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
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Introduction to Fourier optics
TL;DR: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968 as discussed by the authors, with a special emphasis on applications to diffraction, imaging, optical data processing, and holography.
Journal ArticleDOI
Methods of Conjugate Gradients for Solving Linear Systems
TL;DR: An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns and it is shown that this method is a special case of a very general method which also includes Gaussian elimination.
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Field computation by moment methods
TL;DR: This first book to explore the computation of electromagnetic fields by the most popular method for the numerical solution to electromagnetic field problems presents a unified approach to moment methods by employing the concepts of linear spaces and functional analysis.
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