Journal Article10.1016/S0168-9274(98)00025-7
Numerical solution of problems on unbounded domains. a review
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TL;DR: An extensive survey and comparative assessment of different existing methods for constructing the ABCs are presented and a new ABCs technique proposed in recent work is described, which allows one to obtain highly accurate ABCs in the form of certain (nonlocal) boundary operator equations.
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About: This article is published in Applied Numerical Mathematics. The article was published on 01 Aug 1998. The article focuses on the topics: Boundary value problem.
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Citations
Artificial boundary conditions for the numerical simulation of unsteady acoustic waves
TL;DR: In this paper, the authors proposed non-local artificial boundary conditions (ABCs) for the numerical simulation of genuinely time-dependent acoustic waves that propagate from a compact source in an unbounded unobstructed space.
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Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layers
TL;DR: Two main approaches are derived: a Fourier-based pseudospectral method, and a real space method based on an efficient computation of the fractional Laplacian with PML.
Towards accurate artificial boundary conditions for nonlinear PDEs through examples
Xavier Antoine,Christophe Besse,Jeremie Szeftel +2 more
- 01 Sep 2009
TL;DR: A comprehensive review of current developments related to the derivation of artificial boundary conditions for nonlinear partial differential equations is given in this article, where the essential tools to build such boundary conditions are based on pseudodifferential and paradifferential calculus.
New absorbing layers conditions for short water waves
TL;DR: A new PML formulation for the linearized shallow-water equations including the Coriolis force is developed and it is illustrated that it is stable for long-time simulations.
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Analysis of High-Order Absorbing Boundary Conditions for the Schrödinger Equation
TL;DR: In this paper, the numerical solution of Schrodinger equations on an unbounded spatial domain is studied, and the stability of the reduced initial boundary value problem in the computational interval is proved by energy estimate.
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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.
•Book
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.
10.8K
Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes
Antony Jameson,Wolfgang Schmidt,Eli Turkel +2 more
- 01 Jun 1981
TL;DR: In this paper, a new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains.
4.4K