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We present a new boundary integral formulation for time-harmonic wave diffraction from two-dimensional structures with many layers of arbitrary periodic shape, such as multilayer dielectric gratings in TM polarization. Our scheme is robust…

Numerical Analysis · Mathematics 2015-06-23 Min Hyung Cho , Alex H. Barnett

We developed a fast numerical algorithm for solving the three dimensional vectorial Helmholtz equation that arises in electromagnetic scattering problems. The algorithm is based on electric field integral equations and is essentially a…

Computational Physics · Physics 2019-07-24 S. B. Wang , H. H. Zheng , J. J. Xiao , Z. F. Lin , C. T. Chan

We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…

Numerical Analysis · Mathematics 2014-04-10 Kenneth L. Ho , Leslie Greengard

We describe an accelerated direct solver for the integral equations which model acoustic scattering from curved surfaces. Surfaces are specified via a collection of smooth parameterizations given on triangles, a setting which generalizes…

Numerical Analysis · Mathematics 2013-09-02 James Bremer , Adrianna Gillman , Per-Gunnar Martinsson

We consider the simulation of electromagnetic scattering by single and multiple isotropic homogeneous dielectric particles using boundary integral equations. Galerkin discretizations of the classical Poggio-Miller-Chang-Harrington-Wu-Tsai…

Numerical Analysis · Mathematics 2020-05-14 Antigoni Kleanthous , Timo Betcke , David P. Hewett , Matthew W. Scroggs , Anthony J. Baran

We present and analyze fully discrete Nystr\"om methods for the solution of three classes of well conditioned boundary integral equations for the solution of two dimensional scattering problems by homogeneous dielectric scatterers.…

Numerical Analysis · Mathematics 2014-04-07 Y. Boubendir , V. Dominguez , C. Turc

This paper is devoted to the efficient numerical solution of the Helmholtz equation in a two- or three-dimensional rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and…

Numerical Analysis · Computer Science 2019-10-24 Jari Toivanen , Monika Wolfmayr

This paper proposes a new multiple-scattering frequency-time hybrid (FTH-MS) integral equation solver for problems of wave scattering by obstacles in two dimensional space, including interior problems in closed cavities and problems…

Numerical Analysis · Mathematics 2025-07-09 Shuai Pan , Gang Bao , Tao Yin , Oscar P. Bruno

Fast, high-order accurate algorithms for electromagnetic scattering from axisymmetric objects are of great importance when modeling physical phenomena in optics, materials science (e.g. meta-materials), and many other fields of applied…

Numerical Analysis · Mathematics 2019-05-22 Jun Lai , Michael O'Neil

We present a novel approach for the numerical solution of problems of elastic scattering by open arcs in two dimensions. Our methodology relies on the composition of weighted versions of the classical operators associated with Dirichlet and…

Numerical Analysis · Mathematics 2019-02-26 Oscar P. Bruno , Liwei Xu , Tao Yin

The paper describes a numerical method for solving acoustic multibody scattering problems in two and three dimensions. The idea is to compute a highly accurate approximation to the scattering operator for each body through a local…

Numerical Analysis · Mathematics 2026-03-20 Yunhui Cai , Joar Bagge , Per-Gunnar Martinsson

We present a fast iterative solver for scattering problems in 2D, where a penetrable object with compact support is considered. By representing the scattered field as a volume potential in terms of the Green's function, we arrive at the…

Numerical Analysis · Mathematics 2023-03-28 Vaishnavi Gujjula , Sivaram Ambikasaran

This text proposes a fast, rapidly convergent Nystr\"{o}m method for the solution of the Lippmann-Schwinger integral equation that mathematically models the scattering of time-harmonic acoustic waves by inhomogeneous obstacles, while…

Numerical Analysis · Mathematics 2016-03-23 Akash Anand , Ambuj Pandey , B. V. Rathish Kumar , Jagabandhu Paul

This paper proposes a collocation boundary element method based on the Burton--Miller method for solving transmission problems, which is rapidly convergent within the Krylov subspace solver framework. Our study enhances Burton--Miller-type…

Numerical Analysis · Mathematics 2025-01-17 Yasuhiro Matsumoto , Akihiro Yoshiki , Hiroshi Isakari

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…

Numerical Analysis · Mathematics 2016-05-04 Alex. H. Barnett , Bradley J. Nelson , J. Matthew Mahoney

In this paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz decomposition, the elastic scattering problem is reduced to a…

Numerical Analysis · Mathematics 2022-09-14 Heping Dong , Jun Lai , Peijun Li

Consider the scattering of a time-harmonic plane wave by heterogeneous media consisting of linear or nonlinear point scatterers and extended obstacles. A generalized Foldy-Lax formulation is developed to take fully into account of the…

Numerical Analysis · Mathematics 2017-06-22 Jun Lai , Ming Li , Peijun Li , Wei Li

This article deals with boundary integral equation preconditioning for the multiple scattering problem. The focus is put on the single scattering preconditioner, corresponding to the diagonal part of the integral operator, for which two…

Analysis of PDEs · Mathematics 2016-11-28 Bertrand Thierry

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

Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili equation and two-dimensional Toda lattice are investigated on the subject of correct formulation for boundary problem that can be solved within…

Mathematical Physics · Physics 2010-12-17 Vadim Vereschagin