Book Chapter10.1007/978-3-319-19306-9_3
Time Domain Integral Equation Methods in Computational Electromagnetism
Jielin Li,Peter Monk,Daniel S. Weile +2 more
- 01 Jan 2015
- pp 111-189
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TL;DR: This chapter discusses both theoretical and numerical aspects of one approach that solves the stability problem: convolution quadrature, which starts with scattering from a perfectly conducting object and develops the electric field integral equation.
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Abstract: Time domain integral equations have become a major tool in the computational analysis of electromagnetic scattering problems. Classically it was difficult to ensure a stable numerical solution of standard boundary integral formulations of the problem. In this chapter we shall discuss both theoretical and numerical aspects of one approach that solves the stability problem: convolution quadrature. We start with scattering from a perfectly conducting object and develop the electric field integral equation, as well as an error analysis of the fully discrete problem using finite elements in space. After presenting a brief discussion of some special numerical features of this problem, and some numerical results, we move on to scattering by a penetrable object. We end with a general discussion of computational electromagnetism illustrating the role that time domain integral equations can play.
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Citations
A Space-Time Discontinuous Galerkin Trefftz Method for Time Dependent Maxwell's Equations
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43
Monolithic perovskite/c-Si tandem solar cell: Progress on numerical simulation
Chao Gao,Daxue Du,Wenzhong Shen +2 more
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•Dissertation
Time domain boundary integral equation methods in acoustics, heat diffusion and electromagnetism
Tianyu Qiu
- 01 Jan 2016
TL;DR: In this article, the authors analyzed the discretization error induced by the convolution quadrature Galerkin method in seeking the numerical solution to time domain boundary integral equations arising in the problem of acoustic wave scattering by penetrable obstacles, electromagnetic wave scattering and heat conduction in the presence of a bounded inclusion.
9
•Posted Content
New mapping properties of the Time Domain Electric Field Integral Equation
TL;DR: In this paper, the authors show some improved mapping properties of the time domain EDF Integral Equation and its Galerkin semidiscretization in space, using a weak distributional framework with a stronger class of solutions.
6
•Dissertation
Some applications of integral equations to the solution of transient partial differential equations
Matthew E. Hassell
- 01 Jan 2016
TL;DR: In this article, boundary integral methods for solving time-dependent partial differential equations from continuum mechanics were studied, including transient Stokes flow and scalar acoustic scattering by penetrable obstacles.
3
References
Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
Abstract: Maxwell's equations are replaced by a set of finite difference equations. It is shown that if one chooses the field points appropriately, the set of finite difference equations is applicable for a boundary condition involving perfectly conducting surfaces. An example is given of the scattering of an electromagnetic pulse by a perfectly conducting cylinder.
An algorithm for the machine calculation of complex Fourier series
J.W. Cooley,John W. Tukey +1 more
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
A perfectly matched layer for the absorption of electromagnetic waves
TL;DR: Numerical experiments and numerical comparisons show that the PML technique works better than the others in all cases; using it allows to obtain a higher accuracy in some problems and a release of computational requirements in some others.
10.8K
•Book
Advanced engineering electromagnetics
Constantine A. Balanis
- 01 Jan 1989
TL;DR: In this article, the authors introduce the notion of circular cross-section waveguides and cavities, and the moment method is used to compute the wave propagation and polarization.
8K