Journal Article10.1016/J.JCP.2011.09.019
A non-deteriorating algorithm for computational electromagnetism based on quasi-lacunae of Maxwell's equations
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TL;DR: This work proposes a universal algorithm that relies on the Huygens' principle in the generalized form, when a non-zero electrostatic solution can be present behind aft fronts of the propagating waves, i.e., inside the lacunae of Maxwell's equations.
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About: This article is published in Journal of Computational Physics. The article was published on 01 Jan 2012. The article focuses on the topics: Maxwell's equations.
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Citations
The Method of Difference Potentials for the Helmholtz Equation Using Compact High Order Schemes
TL;DR: The combination of the method of difference potentials and compact schemes yields an inexpensive numerical procedure that offers high order accuracy for non-conforming smooth curvilinear boundaries on regular grids.
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Non-deteriorating time domain numerical algorithms for Maxwell's electrodynamics
TL;DR: The main contribution of the current paper is to remove this limitation and modify the algorithm in such a way that one can rather avoid the accumulation of charge all together, which facilitates obtaining the temporally uniform error estimates as in the case of classical lacunae.
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Numerical Solution of 3D Exterior Unsteady Wave Propagation Problems Using Boundary Operators
TL;DR: A boundary method for the numerical simulation of time-dependent waves in three-dimensional (3D) exterior regions and the order of accuracy can be either second or fourth in both space and time.
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A universal framework for non-deteriorating time-domain numerical algorithms in Maxwell's electrodynamics
A. Fedoseyev,E. J. Kansa,Semyon Tsynkov,S. Petropavlovskiy,M. Osintcev,Uri Shumlak,W. D. Henshaw +6 more
- 13 Oct 2016
TL;DR: A developed universal algorithm and software that corrects the long-time deterioration regardless of its origin and how it manifests itself by employing the Huygens’ principle and lacunae of Maxwell's equations.
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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.
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Computational Electrodynamics: The Finite-Difference Time-Domain Method
Allen Taflove
- 31 May 1995
TL;DR: This paper presents background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology, and the proposed three-dimensional Yee algorithm for solving these equations.
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.
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Methods of Mathematical Physics
Richard Courant,David Hilbert +1 more
- 01 Jan 1947
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
8.4K