English
Related papers

Related papers: Near-optimal perfectly matched layers for indefini…

200 papers

We show how to solve time-harmonic wave scattering problems on unbounded domains without truncation. The technique, first developed in numerical relativity for time-domain wave equations, maps the unbounded domain to a bounded domain and…

Numerical Analysis · Mathematics 2021-11-30 Anıl Zenginoğlu

In this paper, we investigate the limiting absorption principle associated to and the well-posedness of the Helmholtz equations with sign changing coefficients which are used to model negative index materials. Using the reflecting technique…

Analysis of PDEs · Mathematics 2015-11-26 Hoai-Minh Nguyen

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

In a multidimensional infinite layer bounded by two hyperplanes, the inhomogeneous Helmholtz equation with a polynomial right-hand side is considered. It is shown that the Dirichlet and Dirichlet-Neumann boundary-value problems with…

Analysis of PDEs · Mathematics 2020-01-28 Oleg D. Algazin

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…

Consider the scattering of a time-harmonic acoustic incident wave by a bounded, penetrable, and isotropic elastic solid, which is immersed in a homogeneous compressible air or fluid. The paper concerns the numerical solution for such an…

Numerical Analysis · Mathematics 2017-03-10 Xue Jiang , Peijun Li

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

This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…

Numerical Analysis · Mathematics 2026-03-10 Long-Ling Du , Zejun Sun , Li-Li Wang , Guang-Hui Zheng

We prove that there are no non-zero square-integrable solutions to a two-dimensional Helmholtz equation in some unbounded inhomogeneous domains which represent junctions of stratified media. More precisely, we consider domains that are…

Analysis of PDEs · Mathematics 2025-04-25 Sarah Al Humaikani , Anne-Sophie Bonnet-Ben Dhia , Sonia Fliss , Christophe Hazard

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

In this paper we present an overview of recent progress on the development and analysis of domain decomposition preconditioners for discretised Helmholtz problems, where the preconditioner is constructed from the corresponding problem with…

Numerical Analysis · Mathematics 2016-06-24 I. G. Graham , E. A. Spence , E. Vainikko

In this paper, we focus on a new wave equation described wave propagation in the attenuation medium. In the first part of this paper, based on the time-domain space fractional wave equation, we formulate the frequency-domain equation named…

Analysis of PDEs · Mathematics 2021-02-23 Junxiong Jia , Shigang Yu , Jigen Peng , Jinghuai Gao

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

Most finite element methods for solving time-harmonic wave-propagation problems lead to a linear system with a non-normal coefficient matrix. The non-normality is due to boundary conditions and losses. One way to solve these systems is to…

Numerical Analysis · Mathematics 2015-06-01 Antti Hannukainen

We leverage the connections between nonexpansive maps, monotone Lipschitz operators, and proximal mappings to obtain near-optimal (i.e., optimal up to poly-log factors in terms of iteration complexity) and parameter-free methods for solving…

Optimization and Control · Mathematics 2020-04-14 Jelena Diakonikolas

Based on the perfectly matched layer (PML) technique, this paper develops a high-accuracy boundary integral equation (BIE) solver for acoustic scattering problems in locally defected layered media in both two and three dimensions. The…

Numerical Analysis · Mathematics 2022-11-03 Wangtao Lu , Liwei Xu , Tao Yin , Lu Zhang

In the aim to find the simplest and most efficient shape of a noise absorbing wall to dissipate the acoustical energy of a sound wave, we consider a frequency model described by the Helmholtz equation with a damping on the boundary. The…

Analysis of PDEs · Mathematics 2020-07-23 Frédéric Magoulès , Thi Phuong Kieu Nguyen , Pascal Omnes , Anna Rozanova-Pierrat

This paper investigates the inverse scattering problem of time-harmonic plane waves incident on a perfectly reflecting random periodic structure. To simulate random perturbations arising from manufacturing defects and surface wear in…

Numerical Analysis · Mathematics 2025-07-29 Zhiqi Sun , Yiwen Lin

The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization…

Optimization and Control · Mathematics 2021-03-30 Konstantin Pieper , Bao Quoc Tang , Philip Trautmann , Daniel Walter

We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…

Analysis of PDEs · Mathematics 2021-03-01 Roland Griesmaier , Bastian Harrach
‹ Prev 1 3 4 5 6 7 10 Next ›