Complex Riemannian metric and absorbing boundary conditions
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TLDR
In this article, it was shown that the boundary layer is non-reflecting when g is flat, that is, the curvature tensor of the complex metric gij is zero.About:
This article is published in Journal de Mathématiques Pures et Appliquées.The article was published on 2001-09-01 and is currently open access. It has received 44 citations till now. The article focuses on the topics: Mixed boundary condition & Perfectly matched layer.read more
Citations
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Solving Time-Harmonic Scattering Problems Based on the Pole Condition II: Convergence of the PML Method
TL;DR: It is proved that the approximate solution obtained by the PML method converges exponentially fast to the true solution in the computational domain as the thickness of the sponge layer tends to infinity.
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A new finite element realization of the perfectly matched layer method for Helmholtz scattering problems on polygonal domains in two dimensions
TL;DR: In this paper, a finite element realization of the Perfectly Matched Layer method (PML-method) is proposed, which allows to deal with a wide class of polygonal domains and with certain types of inhomogeneous exterior domains.
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An Exact Bounded Perfectly Matched Layer for Time-Harmonic Scattering Problems
TL;DR: The aim of this paper is to introduce an “exact” bounded perfectly matched layer (PML) for the scalar Helmholtz equation based on using a nonintegrable absorbing function that can be numerically solved by using standard finite elements.
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Perfectly Matched Layers for time-harmonic second order elliptic problems
TL;DR: The main goal of this work is to give a review of the Perfectly Matched Layer technique for time-harmonic problems, which involve second order elliptic equations writing in divergence form and, in particular, the Helmholtz equation at low frequency regime.
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Leaky modes in twisted microstructured optical fibers
TL;DR: In this paper, the authors investigate the effect of a twist on the losses of leaky modes in micro-structured optical fibers (MOF) using a helicoidal system of coordinates to define the structure and to set up the problem.
References
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Journal ArticleDOI
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.
Book
Inverse Acoustic and Electromagnetic Scattering Theory
David Colton,Rainer Kress +1 more
TL;DR: Inverse Medium Problem (IMP) as discussed by the authors is a generalization of the Helmholtz Equation for direct acoustical obstacle scattering in an Inhomogeneous Medium (IMM).
Journal ArticleDOI
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
Book
Integral equation methods in scattering theory
David Colton,Rainer Kress +1 more
TL;DR: In this article, the Riesz-Fredholm theory for compact operators is applied to boundary-value problems for the scalar Helmholtz equation and the time-harmonic Maxwell equations.
Book
Introduction to symplectic topology
Dusa McDuff,Dietmar Salamon +1 more
TL;DR: In this article, the authors present a survey of the history of classical and modern manifold geometry, from classical to modern, including linear and almost complex structures, and the Arnold conjecture of the group of symplectomorphisms.
Related Papers (5)
A 3D perfectly matched medium from modified maxwell's equations with stretched coordinates
Weng Cho Chew,W.H. Weedon +1 more