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Boundary integral equation is derived for the problem of scattering of electromagnetic waves by 3D homogeneous body of arbitrary shape.

Mathematical Physics · Physics 2009-09-04 A. G. Ramm

We introduce a space-time Trefftz discontinuous Galerkin method for the first-order transient acoustic wave equations in arbitrary space dimensions, extending the one dimensional scheme of Kretzschmar et al. (2016, IMA J. Numer. Anal., 36,…

Numerical Analysis · Mathematics 2022-08-29 Andrea Moiola , Ilaria Perugia

The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the…

Mathematical Physics · Physics 2010-11-09 Evgeny Lakshtanov , Boris Vainberg

This paper proposes and analyzes a full discretization of the exterior transient Stokes problem with Dirichlet boundary conditions. The method is based on a single layer boundary integral representation, using Galerkin semidiscretization in…

Numerical Analysis · Mathematics 2014-10-14 Constantin Bacuta , Matthew E. Hassell , George C. Hsiao , Francisco-Javier Sayas

In this paper, a new type of the discrete fractional Gr{\"o}nwall inequality is developed, which is applied to analyze the stability and convergence of a Galerkin spectral method for a linear time-fractional subdiffusion equation. Based on…

Numerical Analysis · Mathematics 2024-12-20 Yubo Yang , Fanhai Zeng

In geophysical environments, wave motions that are shaped by the action of gravity and global rotation bear the name of gravito-inertial waves. We present a geometrical description of gravito-inertial surface waves, which are low-frequency…

Analysis of PDEs · Mathematics 2026-04-21 Yves Colin de Verdière , Jérémie Vidal

Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…

Mathematical Physics · Physics 2011-05-10 Alexander G. Ramm

The semidiscretization of a sound soft scattering problem modelled by the wave equation is analyzed. The spatial treatment is done by integral equation methods. Two temporal discretizations based on Runge-Kutta convolution quadrature are…

Numerical Analysis · Mathematics 2024-07-25 Jens Markus Melenk , Alexander Rieder

We study Hibridizable Discontinuous Galerkin (HDG) discretizations for a class of non-linear interior elliptic boundary value problems posed in curved domains where both the source term and the diffusion coefficient are non-linear. We…

Numerical Analysis · Mathematics 2021-12-30 Nestor Sánchez , Tonatiuh Sánchez-Vizuet , Manuel E. Solano

The full discretization of the semi-linear stochastic wave equation is considered. The discontinuous Galerkin finite element method is used in space and analyzed in a semigroup framework, and an explicit stochastic position Verlet scheme is…

Numerical Analysis · Mathematics 2020-09-17 Lehel Banjai , Gabriel Lord , Jeta Molla

This paper studies time-dependent electromagnetic scattering from metamaterials that are described by dispersive material laws. We consider the numerical treatment of a scattering problem in which a dispersive material law, for a causal and…

Numerical Analysis · Mathematics 2023-11-08 Jörg Nick , Selina Burkhard , Christian Lubich

In this paper we present a convergence analysis for the Nystrom method proposed in [Jour. Comput. Phys. 169 pp. 2921-2934, 2001] for the solution of the combined boundary integral equation formulations of sound-soft acoustic scattering…

Numerical Analysis · Mathematics 2012-10-12 Oscar P. Bruno , Victor Dominguez , Francisco-Javier Sayas

In the formulation of the problem of scattering of monochromatic waves and the numerical simulation of the solution to the Helmholtz equation, there is a computational inconvenience: the calculation is performed on a finite grid of…

Plasma Physics · Physics 2023-01-20 Vladimir V. Gorin

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…

Analysis of PDEs · Mathematics 2009-12-16 Xiaodong Liu , Bo Zhang

This paper is concerned with the reconstruction of the shape of an acoustic obstacle. Based on the use of the tapered waves with very narrow widths illuminating the obstacle, the boundary of the obstacle is reconstructed by a direct imaging…

Numerical Analysis · Mathematics 2024-10-10 Deyue Zhang , Mengjiao Bai , Yan Chang , Yukun Guo

In two and three dimension we analyze discontinuous Galerkin methods for the acoustic problem. The acoustic fluid that we consider on this paper is inviscid, leading to a linear eigenvalue problem. The acoustic problem is written, in first…

Numerical Analysis · Mathematics 2022-12-09 Felipe Lepe , David Mora , Jesus Vellojin

This paper studies a non-singular coupling scheme for solving the acoustic and elastic wave scattering problems and its extension to the problems of Laplace and Lam\'e equations and the problem with a compactly supported inhomogeneity is…

Numerical Analysis · Mathematics 2023-12-27 Xiaojuan Liu , Maojun Li , Tao Yin

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

A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial…

Numerical Analysis · Mathematics 2022-05-11 Vincenzo Gulizzi , Robert Saye

This paper investigates the asymptotic behaviors of time-harmonic acoustic waves generated by an incident wave illuminating inhomogeneous medium inclusions with high-contrast material parameters. We derive sharp asymptotic estimates and…

Analysis of PDEs · Mathematics 2024-10-31 Yueguang Hu , Hongyu Liu