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Related papers: Perfectly Matched Layers for Coupled Nonlinear Sch…

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In outdoor acoustics, the calculations of sound propagating in air can be computationally heavy if the domain is chosen large enough to fulfil the Sommerfeld radiation condition. By strategically truncating the computational domain with a…

The design of absorbing boundary conditions (ABC) in a numerical simulation is a challenging task. In the best cases, spurious reflections remain for some angles of incidence or at certain wave lengths. In the worst, ABC are not even…

Computational Physics · Physics 2024-09-11 Guillaume Bouchard , Arnaud Beck , Francesco Massimo , Arnd Specka

This work is a contribution to the understanding of the question of stability of Perfectly Matched Layers (PMLs) in corners, at continuous and discrete levels. First, stability results are presented for the Cartesian PMLs associated to a…

Numerical Analysis · Mathematics 2011-05-17 Eliane Bécache , Andres Prieto

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems…

Analysis of PDEs · Mathematics 2021-02-04 Changkun Wei , Jiaqing Yang , Bo Zhang

The main task in this paper is to prove that the perfectly matched layers (PML) method converges exponentially with respect to the PML parameter, for scattering problems with periodic surfaces. In [5], a linear convergence is proved for the…

Numerical Analysis · Mathematics 2021-09-02 Ruming Zhang

We study overlapping Schwarz methods for the Helmholtz equation posed in any dimension with large, real wavenumber and smooth variable wave speed. The radiation condition is approximated by a Cartesian perfectly-matched layer (PML). The…

Numerical Analysis · Mathematics 2024-04-03 Jeffrey Galkowski , Shihua Gong , Ivan G. Graham , David Lafontaine , Euan A. Spence

The perfectly matched layer(PML) is commonly used in wave propagation, radiation and diffraction problems in unbounded space domains. A new implementation scheme of PML is presented. The PML formulation is pre-defined, and the wave field…

Geophysics · Physics 2024-04-24 Yuqin Luo , Xintong Dong , Shiqi Dong , Tie Zhong , Yu Zhang , Ying Wang , Ning Hu

Consider the interaction of biharmonic waves with a periodic array of cavities, characterized by the Kirchhoff--Love model. This paper investigates the perfectly matched layer (PML) formulation and its numerical soution to the governing…

Numerical Analysis · Mathematics 2024-04-23 Peijun Li , Xiaokai Yuan

We construct a perfectly matched absorbing layer for stationary Schrodinger equation with analytic slowly decaying potential in a periodic structure. We prove the unique solvability of the problem with perfectly matched layer of finite…

Mathematical Physics · Physics 2011-02-17 Victor Kalvin

This paper presents a stable finite element approximation for the acoustic wave equation on second-order form, with perfectly matched layers (PML) at the boundaries. Energy estimates are derived for varying PML damping for both the discrete…

Numerical Analysis · Mathematics 2022-06-20 Gustav Ludvigsson , Kenneth Duru , Gunilla Kreiss

Perfectly transparent metamaterial structures of arbitrary shapes, constructed from coordinate stretching and contractions, are presented. Coordinate stretching has been used for 2 decades in perfectly matched layers (PMLs) to…

Optics · Physics 2016-02-16 Nima Chamanara , Christophe Caloz

An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…

Numerical Analysis · Mathematics 2016-05-30 Xue Jiang , Peijun Li , Junliang Lv , Weiying Zheng

For some anisotropic wave models, the PML (perfectly matched layer) method of open boundaries can become polynomially or exponentially unstable in time. In this work we present a new method of open boundaries, the phase space filter, which…

Numerical Analysis · Mathematics 2008-05-20 Avy Soffer , Chris Stucchio

This article proves the well posedness of the boundary value problemthat arises when PML algorithms are applied to Pauli's equationswith a three dimensional rectangle as computational domain. The absorptionsare positive near the boundary…

Analysis of PDEs · Mathematics 2022-02-18 Laurence Halpern , Jeffrey Rauch

Perfectly matched layers are a very efficient and accurate way to absorb waves in media. We present a stable convolutional unsplit perfectly matched formulation designed for the linearized stratified Euler equations. However, the technique…

Solar and Stellar Astrophysics · Physics 2015-05-18 S. M. Hanasoge , D. Komatitsch , L. Gizon

We consider a system of two discrete nonlinear Schr\"{o}dinger equations, coupled by nonlinear and linear terms. For various physically relevant cases, we derive a modulational instability criterion for plane-wave solutions. We also find…

Soft Condensed Matter · Physics 2015-06-24 Z. Rapti , A. Trombettoni , P. G. Kevrekidis , D. J. Frantzeskakis , Boris A. Malomed , A. R. Bishop

We introduce a new additive sweeping preconditioner for the Helmholtz equation based on the perfect matched layer (PML). This method divides the domain of interest into thin layers and proposes a new transmission condition between the…

Numerical Analysis · Mathematics 2016-03-17 Fei Liu , Lexing Ying

In the author's previous paper (Zhang et al. 2022), exponential convergence was proved for the perfectly matched layers (PML) approximation of scattering problems with periodic surfaces in 2D. However, due to the overlapping of…

Numerical Analysis · Mathematics 2024-01-02 Ruming Zhang

This paper introduces a new sweeping preconditioner for the iterative solution of the variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow the general structure of constructing an approximate $LDL^t$…

Numerical Analysis · Mathematics 2010-08-03 Björn Engquist , Lexing Ying

This paper considers the scattering of a time-harmonic acoustic plane wave by an elastic body with an unbounded periodic surface. The original problem can be confined to the analysis of the fields in one periodic cell. With the help of the…

Numerical Analysis · Mathematics 2026-02-11 Sijia Li , Lei Lin , Junliang Lv