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This paper introduces planewave density interpolation methods for the regularization of weakly singular, strongly singular, hypersingular and nearly singular integral kernels present in 3D Helmholtz surface layer potentials and associated…

Numerical Analysis · Mathematics 2024-12-20 Carlos Pérez-Arancibia , Catalin Turc , Luiz Faria

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

In this paper we consider high-frequency acoustic transmission problems with jumping coefficients modelled by Helmholtz equations. The solution then is highly oscillatory and, in addition, may be localized in a very small vicinity of…

Numerical Analysis · Mathematics 2025-03-03 Silvia Falletta , Stefan Sauter

We present an efficient method to solve scattering problems in two-dimensional open billiards with two leads and a complicated scattering region. The basic idea is to transform the scattering region to a rectangle, which will lead to…

Quantum Physics · Physics 2009-11-13 Gursoy B. Akguc , Thomas H. Seligman

Most problems in electrodynamics do not have an analytical solution so much effort has been put in the development of numerical schemes, such as the finite-difference method, volume element methods, boundary element methods, and related…

Numerical Analysis · Mathematics 2023-01-03 L. Ponzellini Marinelli , L. Raviola

We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…

Differential Geometry · Mathematics 2025-06-11 Eric Schippers , Wolfgang Staubach

The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the…

Numerical Analysis · Mathematics 2014-09-17 Lexing Ying

This paper gives a remark on the Enclosure Method by considering inverse obstacle scattering problems with a single incident wave whose governing equation is given by the Helmholtz equation in two dimensions. It is concerned with the…

Analysis of PDEs · Mathematics 2011-09-21 Masaru Ikehata

We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth, strictly convex obstacles with Neumann boundary conditions. Using integral equation…

Numerical Analysis · Mathematics 2022-08-15 Yassine Boubendir , Fatih Ecevit

A new approach is introduced for deriving a mixed variational formulation for Kirchhoff plate bending problems with mixed boundary conditions involving clamped, simply supported, and free boundary parts. Based on a regular decomposition of…

Numerical Analysis · Mathematics 2017-12-21 Katharina Rafetseder , Walter Zulehner

We present a new complexification scheme based on the classical double layer potential for the solution of the Helmholtz equation with Dirichlet boundary conditions in compactly perturbed half-spaces in two and three dimensions. The kernel…

Numerical Analysis · Mathematics 2025-01-07 Charles L. Epstein , Leslie Greengard , Jeremy Hoskins , Shidong Jiang , Manas Rachh

We consider the scattering problem governed by the Helmholtz equation with inhomogeneity in both `conductivity' in the divergence form and `potential' in the lower order term. The support of the inhomogeneity is assumed to contain a convex…

Analysis of PDEs · Mathematics 2020-09-14 Fioralba Cakoni , Jingni Xiao

In this paper we consider the electromagnetic scattering problem by an obstacle characterised by a Generalized Impedance Boundary Condition in the harmonic regime. These boundary conditions are well known to provide accurate models for thin…

Analysis of PDEs · Mathematics 2013-12-05 Nicolas Chaulet

Consider the scattering of a time-harmonic acoustic plane wave by a bounded elastic obstacle which is immersed in a homogeneous acoustic medium. This paper concerns an inverse acoustic-elastic interaction problem, which is to determine the…

Numerical Analysis · Mathematics 2020-04-22 Heping Dong , Jun Lai , Peijun Li

This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…

Numerical Analysis · Mathematics 2023-10-13 Yan Chang , Yukun Guo , Hongyu Liu , Deyue Zhang

A system of boundary-domain integral equations is derived from the bidimensional Dirichlet problem for the diffusion equation with variable coefficient using the novel parametrix from [22] different from the one in [5,18]. Mapping…

Analysis of PDEs · Mathematics 2020-11-23 C. F. Portillo , Z. W. Woldemicheal

In this paper, we propose a new numerical method for scattering problems in periodic waveguide, based on the newly established contour integral representation of solutions in a previous paper by the author (see [Zhadf]). For this kind of…

Numerical Analysis · Mathematics 2021-04-30 Ruming Zhang

We consider solving the exterior Dirichlet problem for the Helmholtz equation with the $h$-version of the boundary element method (BEM) using the standard second-kind combined-field integral equations. We prove a new, sharp bound on how the…

Numerical Analysis · Mathematics 2019-02-25 Jeffrey Galkowski , Eike H. Müller , Euan A. Spence

Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of…

Mathematical Physics · Physics 2011-03-11 Anton Krynkin , Olga Umnova , Alvin Y. B. Chong , Shahram Taherzadeh , Keith Attenborough

Numerically solving the 2D Helmholtz equation is widely known to be very difficult largely due to its highly oscillatory solution, which brings about the pollution effect. A very fine mesh size is necessary to deal with a large wavenumber…

Analysis of PDEs · Mathematics 2022-05-17 Bin Han , Michelle Michelle