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We examine the use of a two-level deflation preconditioner combined with GMRES to locally solve the subdomain systems arising from applying domain decomposition methods to Helmholtz problems. Our results show that the direct solution method…

Numerical Analysis · Mathematics 2023-05-03 Niall Bootland , Vandana Dwarka , Pierre Jolivet , Victorita Dolean , Cornelis Vuik

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

We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…

Fluid Dynamics · Physics 2017-01-23 Luiz M. Faria , Rodolfo R. Rosales

The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…

Implicit solvers for atmospheric models are often accelerated via the solution of a preconditioned system. For block preconditioners this typically involves the factorisation of the (approximate) Jacobian resulting from linearization of the…

Numerical Analysis · Mathematics 2024-10-03 David Lee , Alberto F. Martín , Kieran Ricardo

For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation…

Numerical Analysis · Mathematics 2018-04-24 Wangtao Lu , Ya Yan Lu , Jianliang Qian

The Helmholtz scattering problem with high wave number is truncated by the perfectly matched layer (PML) technique and then discretized by the linear continuous interior penalty finite element method (CIP-FEM). It is proved that the…

Numerical Analysis · Mathematics 2018-06-26 Yonglin Li , Haijun Wu

This paper studies the PML method for wave scattering in a half space of homogeneous medium bounded by a two-dimensional, perfectly conducting, and locally defected periodic surface, and develops a high-accuracy boundary-integral-equation…

Numerical Analysis · Mathematics 2021-08-03 Xiuchen Yu , Guanghui Hu , Wangtao Lu , Andreas Rathsfeld

This paper addresses the efficient solution of linear systems arising from curl-conforming finite element discretizations of $H(\mathrm{curl})$ elliptic problems with heterogeneous coefficients. We first employ the discrete form of a…

Numerical Analysis · Mathematics 2025-06-10 Chupeng Ma , Yongwei Zhang

A two-step preconditioned iterative method based on the Hermitian/Skew-Hermitian splitting is applied to the solution of nonsymmetric linear systems arising from the Finite Element approximation of convection-diffusion equations. The…

Numerical Analysis · Mathematics 2008-07-23 Alessandro Russo , Cristina Tablino Possio

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 use the Method of Difference Potentials (MDP) to solve a non-overlapping domain decomposition formulation of the Helmholtz equation. The MDP reduces the Helmholtz equation on each subdomain to a Calderon's boundary equation with…

Numerical Analysis · Mathematics 2021-03-24 Evan North , Semyon Tsynkov , Eli Turkel

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 introduces a new boundary element formulation for transient electromagnetic scattering by homogeneous dielectric objects based on the time-domain PMCHWT equation. To address dense-mesh breakdown, a multiplicative Calderon…

Systems and Control · Electrical Eng. & Systems 2025-10-10 Van Chien Le , Cedric Munger , Francesco P. Andriulli , Kristof Cools

In this work, we present a new solution representation for the Helmholtz transmission problem in a bounded domain in $\mathbb{R}^2$ with a thin and periodic layer of finite length. The layer may consists of a periodic pertubation of the…

Analysis of PDEs · Mathematics 2017-06-23 Adrien Semin , Bérangère Delourme , Kersten Schmidt

Multigrid preconditioners and solvers for the indefinite Helmholtz equation suffer from non-stability of the stationary smoothers due to the indefinite spectrum of the operator. In this paper we explore GMRES as a replacement for the…

Numerical Analysis · Computer Science 2015-03-17 Bram Reps , Wim Vanroose , Hisham bin Zubair

We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph…

Numerical Analysis · Mathematics 2026-03-11 Stephan Köhler , Oliver Rheinbach , Yue Xiang Tee , Sebastian Zug

We consider a scalar wave propagation in harmonic regime modelled by Helmholtz equation with heterogeneous coefficients. Using the Multi-Trace Formalism (MTF), we propose a new variant of the Optimized Schwarz Method (OSM) that can…

Analysis of PDEs · Mathematics 2019-10-14 Xavier Claeys

This paper is concerned with the time-domain stochastic acoustic scattering problem driven by a spatially white additive Gaussian noise. The main contributions of the work are twofold. First, we prove the existence and uniqueness of the…

Numerical Analysis · Mathematics 2025-08-19 Hongxia Guo , Tianjiao Wang , Xiang Xu , Yue Zhao

This paper is concerned with the thermoelastic obstacle scattering problem in three dimensions. A uniaxial perfectly matched layer (PML) method is firstly introduced to truncate the unbounded scattering problem, leading to a truncated PML…

Analysis of PDEs · Mathematics 2026-02-06 Qianyuan Yin , Changkun Wei , Bo Zhang