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In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for…

Computational Physics · Physics 2018-02-07 Andre Diatta , Muamer Kadic , Martin Wegener , Sebastien Guenneau

We consider a wide variety of scattering problems including scattering by Dirichlet, Neumann, and penetrable obstacles. We consider a radial perfectly-matched layer (PML) and show that for any PML width and a steep-enough scaling angle, the…

Analysis of PDEs · Mathematics 2023-01-31 Jeffrey Galkowski , David Lafontaine , Euan A. Spence

This paper constructs perfectly matched layers (PML) for a system of 2D Coupled Nonlinear Schr\"odinger equations with mixed derivatives which arises in the modeling of gap solitons in nonlinear periodic structures with a non-separable…

Numerical Analysis · Mathematics 2015-05-13 Tomáš Dohnal

Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions of this linear system is to choose an efficient solver. In…

Numerical Analysis · Mathematics 2023-01-31 Sahar Borzooei , Victorita Dolean , Pierre-Henri Tournier , Claire Migliaccio

The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…

Analysis of PDEs · Mathematics 2016-04-27 Yixian Gao , Peijun Li

Wrapping a computation domain with a perfectly matched layer (PML) is one of the most effective methods of imitating/approximating the radiation boundary condition in Maxwell and wave equation solvers. Many PML implementations often use a…

Numerical Analysis · Mathematics 2021-09-03 Liang Chen , Mehmet Burak Ozakin , Shehab Ahmed , Hakan Bagci

We prove stability and exponential convergence of the Perfectly Matched Layer (PML) method for acoustic scattering on manifolds with axial analytic quasicylindrical ends. These manifolds model long-range geometric perturbations (e.g.…

Analysis of PDEs · Mathematics 2014-07-23 Victor Kalvin

We propose and analyze the perfectly matched layer (PML) method for the time-harmonic acoustic waves driven by the white noise source in the presence of the uniform flow. A PML is an artificial absorbing layer commonly used to truncate…

Analysis of PDEs · Mathematics 2015-06-10 Sang-Hyeon Park , Imbo Sim

A Finite-Difference Time-Domain (FDTD) scheme with Perfectly Matched Layers (PMLs) is considered for solving the time-dependent Schr\"{o}dinger equation, and simulate the ionization of an electron initially bound to a one-dimensional…

Mesoscale and Nanoscale Physics · Physics 2020-04-02 Høgni C. Kamban , Sigurd S. Christensen , Thomas Søndergaard , Thomas G. Pedersen

A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D Helmholtz equations. Transmission conditions based on the perfectly matched layer (PML) are derived that avoid artificial reflections and match incoming and…

Numerical Analysis · Mathematics 2013-06-24 Christiaan C. Stolk

Numerical simulation of wave propagation in an infinite medium is made possible by surrounding a finite region by a perfectly matched layer (PML). Using this approach a generalized three-dimensional (3D) formulation is proposed for…

Numerical Analysis · Mathematics 2016-12-21 Hisham Assi , Richard S. C. Cobbold

A nonlocal perfectly matched layer (PML) is formulated for the nonlocal wave equation in the whole real axis and numerical discretization is designed for solving the reduced PML problem on a bounded domain. The nonlocal PML poses challenges…

Numerical Analysis · Mathematics 2022-02-22 Yu Du , Jiwei Zhang

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

We consider the scalar anisotropic wave equation. Recently a convergence analysis for radial perfectly matched layers (PML) in the frequency domain was reported and in the present article we continue this approach into the time domain.…

Numerical Analysis · Mathematics 2024-11-28 Martin Halla , Maryna Kachanovska , Markus Wess

This paper proposes a new boundary integral equation (BIE) methodology based on the perfectly matched layer (PML) truncation technique for solving the electromagnetic scattering problems in a multi-layered medium. Instead of using the…

Numerical Analysis · Mathematics 2024-01-30 Gang Bao , Wangtao Lu , Tao Yin , Lu Zhang

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

We present a stable discontinuous Galerkin (DG) method with a perfectly matched layer (PML) for three and two space dimensional linear elastodynamics, in velocity-stress formulation, subject to well-posed linear boundary conditions. First,…

Numerical Analysis · Mathematics 2020-01-08 Kenneth Duru , Leonhard Rannabauer , Alice-Agnes Gabriel , Gunilla Kreiss , Michael Bader

Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…

Optics · Physics 2009-11-10 Diana C. Skigin

Perfectly Matched Layer (PML) is a widely adopted non-reflecting boundary treatment for wave simulations. Reducing numerical reflections from a discretized PML has been a long lasting challenge. This paper presents a new discrete PML for…

Numerical Analysis · Mathematics 2019-03-12 Albert Chern

It is known that any {\em real coordinate transformation} (RCT) to compress waves in an unbounded domain into a bounded domain results in infinite oscillations that cannot be resolved by any grid-based method. In this paper, we intend to…

Numerical Analysis · Mathematics 2024-01-30 Jiangxing Wang , Lilian Wang , Bo Wang