English
Related papers

Related papers: Generalised eigenfunction expansion and singularit…

200 papers

We study sound-soft time-harmonic acoustic scattering by general scatterers, including fractal scatterers, in 2D and 3D space. For an arbitrary compact scatterer $\Gamma$ we reformulate the Dirichlet boundary value problem for the Helmholtz…

Numerical Analysis · Mathematics 2026-03-10 A. M. Caetano , S. N. Chandler-Wilde , X. Claeys , A. Gibbs , D. P. Hewett , A. Moiola

The generalized Benjamin-Bona-Mahony equation (gBBM) is a model for nonlinear dispersive waves which, in the long-wave limit, is approximately equivalent to the generalized Korteweg-de Vries equation (gKdV). While the long-time behaviour of…

Analysis of PDEs · Mathematics 2024-02-19 A. George Morgan

The scattering process of a dynamic perturbation impinging on a draining-tub model of an acoustic black hole is numerically solved in the time domain. Analogies with real black holes of General Relativity are explored by using recently…

General Relativity and Quantum Cosmology · Physics 2009-11-11 C. Cherubini , F. Federici , S. Succi , M. P. Tosi

Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities…

Numerical Analysis · Mathematics 2019-02-20 Ching-Shan Chou , Yukun Li , Dongbin Xiu

A periodizing scheme and the method of fundamental solutions are used to solve acoustic wave scattering from doubly-periodic three-dimensional multilayered media. A scattered wave in a unit cell is represented by the sum of the near and…

Numerical Analysis · Mathematics 2019-06-26 Min Hyung Cho

In this paper, we develop an efficient spectral-Galerkin-type search extension method (SGSEM) for finding multiple solutions to semilinear elliptic boundary value problems. This method constructs effective initial data for multiple…

Numerical Analysis · Mathematics 2023-08-15 Wei Liu , Ziqing Xie , Yongjun Yuan

This work is concerned with a unique combination of high order local absorbing boundary conditions (ABC) with a general curvilinear Finite Element Method (FEM) and its implementation in Isogeometric Analysis (IGA) for time-harmonic acoustic…

Numerical Analysis · Mathematics 2019-03-27 Tahsin Khajah , Vianey Villamizar

Electromagnetic (EM) wave scattering by many parallel infinite cylinders is studied asymptotically as a tends to 0, where a is the radius of the cylinders. It is assumed that the centres of the cylinders are distributed so that their…

Computational Physics · Physics 2015-06-05 A. G. Ramm , M. I. Andriychuk

The Generalized Method of Moments (GMM) is a partition of unity based technique for solving electromagnetic and acoustic boundary integral equations. Past work on the GMM for electromagnetics was confined to geometries modeled by piecewise…

Computational Physics · Physics 2015-06-18 Daniel Dault , Naveen V. Nair , Jie Li , Balasubramaniam Shanker

In the frame of volume integral equation methods, we introduce an alternative representation of the electromagnetic field scattered by a homogeneous object of arbitrary shape at a given frequency, in terms of a set of modes independent of…

We consider time domain acoustic scattering from a penetrable medium with a variable sound speed. This problem can be reduced to solving a time domain volume Lippmann-Schwinger integral equation. Using convolution quadrature in time and…

Numerical Analysis · Mathematics 2014-07-30 Armin Lechleiter , Peter Monk

This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a single-layer ansatz. The integral equation is discretized by…

Numerical Analysis · Mathematics 2025-09-05 Théophile Chaumont-Frelet , Heiko Gimperlein , Ignacio Labarca-Figueroa , Jörg Nick

This work describes and analyzes the domain derivative for a time-dependent acoustic scattering problem. We study the nonlinear operator that maps a sound-soft scattering object to the solution of the time-dependent wave equation evaluated…

Numerical Analysis · Mathematics 2025-10-27 Marvin Knöller , Jörg Nick

The numerical simulation of acoustic waves in complex 3D media is a key topic in many branches of science, from exploration geophysics to non-destructive testing and medical imaging. With the drastic increase in computing capabilities this…

Computational Physics · Physics 2016-12-21 Alexis Bottero , Paul Cristini , Dimitri Komatitsch , Mark Asch

We consider time-harmonic electromagnetic scattering problems on perfectly conducting scatterers with uncertain shape. Thus, the scattered field will also be uncertain. Based on the knowledge of the two-point correlation of the domain…

Numerical Analysis · Mathematics 2019-07-15 Jürgen Dölz

We develop a convergence theory of space-time discretizations for the linear, 2nd-order wave equation in polygonal domains $\Omega\subset\mathbb{R}^2$, possibly occupied by piecewise homogeneous media with different propagation speeds.…

Numerical Analysis · Mathematics 2022-08-29 Pratyuksh Bansal , Andrea Moiola , Ilaria Perugia , Christoph Schwab

A generalized finite element method is proposed for solving a heterogeneous reaction-diffusion equation with a singular perturbation parameter $\varepsilon$, based on locally approximating the solution on each subdomain by solution of a…

Numerical Analysis · Mathematics 2024-07-25 Chupeng Ma , Jens Markus Melenk

We consider acoustic scattering in heterogeneous media with piecewise constant wave number. The discretization is carried out using a Galerkin boundary element method in space and Runge-Kutta convolution quadrature in time. We prove…

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

We analyse and implement a quasi-Monte Carlo (QMC) finite element method (FEM) for the forward problem of uncertainty quantification (UQ) for the Helmholtz equation with random coefficients, both in the second-order and zero-order terms of…

Numerical Analysis · Mathematics 2025-11-04 Ivan G. Graham , Frances Y. Kuo , Dirk Nuyens , Ian H. Sloan , Euan A. Spence

We present a time domain method to solve quantum scattering by an arbitrary potential of finite range. The scattering wave function in full space can be obtained, including the near field, the mid field (i.e. Fresnel region) and the far…

Quantum Physics · Physics 2024-12-31 Kun Chen