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
On the use of complex stretching coordinates in generalized finite difference method with applications in inhomogeneous visco-elasto dynamics
TL;DR: In this paper, an approach is proposed for the evaluation of complex derivatives directly in terms of complex stretching coordinates of points in PML. For doing this within the framework of generalized finite difference method (GFDM), a difference equation is formulated and presented, where both the function values and coordinates of data points might be complex.
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Artificial boundary conditions for simulations of seismic air-gun bubbles
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- 01 Jan 2015
TL;DR: The most commonly used seismic source is the seismic air gun, which is a canister containing highly compressed air, forming an oscillating bubble as discussed by the authors, and the air is released into the sea, forming a wave wave through the sea.
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The reduced scalar potential in regions with permeable materials: Reasons for loss of accuracy and cancellation
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TL;DR: In this article, the authors investigate theoretically the underlying reasons for this lack of accuracy in permeable regions when using the reduced scalar potential (RSP) as a unique potential, leading to an efficient numerical method to compute the magnetic field in regions with high magnetic permeability.
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Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical type
TL;DR: In this paper, a new method is presented to construct local artificial boundary conditions for a very general class of elliptic problems where the main asymptotic term is not known explicitly.
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References
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Allen Taflove
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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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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.
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