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We study the Darcy boundary value problem with log-normal permeability field. We adopt a perturbation approach, expanding the solution in Taylor series around the nominal value of the coefficient, and approximating the expected value of the…

Numerical Analysis · Mathematics 2020-05-15 Francesca Bonizzoni , Fabio Nobile

This paper is concerned with solving the Helmholtz exterior Dirichlet and Neumann problems with large wavenumber $k$ and smooth obstacles using the standard second-kind boundary integral equations. We consider Galerkin and collocation…

Numerical Analysis · Mathematics 2026-03-24 Jeffrey Galkowski , Manas Rachh , Euan A. Spence

This paper aims to address two issues of integral equations for the scattering of time-harmonic electromagnetic waves by a perfect electric conductor with Lipschitz continuous boundary: ill-conditioned {boundary element Galerkin matrices}…

Numerical Analysis · Mathematics 2024-10-29 Van Chien Le , Kristof Cools

This paper is concerned with the numerical computation of scattering resonances of the Laplacian for Dirichlet obstacles with rough boundary. We prove that under mild geometric assumptions on the obstacle there exists an algorithm whose…

Numerical Analysis · Mathematics 2024-02-02 Frank Rösler , Alexei Stepanenko

In this paper, we focus on a new wave equation described wave propagation in the attenuation medium. In the first part of this paper, based on the time-domain space fractional wave equation, we formulate the frequency-domain equation named…

Analysis of PDEs · Mathematics 2021-02-23 Junxiong Jia , Shigang Yu , Jigen Peng , Jinghuai Gao

In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…

Numerical Analysis · Mathematics 2015-04-08 Bangti Jin , Raytcho Lazarov , Dongwoo Sheen , Zhi Zhou

This work considers a time domain inverse acoustic obstacle scattering problem due to passive data. Motivated by the Helmholtz-Kirchhoff identity in the frequency domain, we propose to relate the time domain measurement data in passive…

Numerical Analysis · Mathematics 2025-06-03 Xiaoli Liu , Shixu Meng , Jialu Tian , Bo Zhang

We consider the initial boundary value problem for the time-fractional diffusion equation with a homogeneous Dirichlet boundary condition and an inhomogeneous initial data $a(x)\in L^{2}(D)$ in a bounded domain $D\subset \mathbb{R}^d$ with…

Numerical Analysis · Mathematics 2020-02-19 Jiuhua Hu , Guanglian Li

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

Consider the time-harmonic acoustic scattering from a bounded penetrable obstacle imbedded in an isotropic homogeneous medium. The obstacle is supposed to possess a circular conic point or an edge point on the boundary in three dimensions…

Analysis of PDEs · Mathematics 2018-01-17 Johannes Elschner , Guanghui Hu

In this article, we consider the solution to elliptic diffusion problems on a class of random domains obtained by log-Gaussian random homothety of the unit disk respectively an annulus. We model the problem under consideration and verify…

Numerical Analysis · Mathematics 2026-03-26 Dinh Dũng , Helmut Harbrecht , Van Kien Nguyen , Christoph Schwab

We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulated via projectors onto outgoing modes determine the…

Numerical Analysis · Mathematics 2025-09-26 Tristan Goodwill , Shidong Jiang , Manas Rachh , Kosuke Sugita

This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electromagnetic wave propagation is modeled by a boundary value…

Numerical Analysis · Mathematics 2022-02-21 Gang Bao , Mingming Zhang , Xue Jiang , Peijun Li , Xiaokai Yuan

Considering fractional fast diffusion equations on bounded open polyhedral domains in $\mathbb{R}^N$, we give a fully Galerkin approximation of the solutions by $C^0$-piecewise linear finite elements in space and backward Euler…

Numerical Analysis · Mathematics 2019-12-18 Dongxue Li , Youquan Zheng

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

We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…

Numerical Analysis · Mathematics 2015-06-18 Bangti Jin , Raytcho Lazarov , Yikan Liu , Zhi Zhou

We propose a modified Trefftz Discontinuous Galerkin (TDG) method for approximating a time-harmonic acoustic scattering problem in an infinitely elongated waveguide. In the waveguide we suppose there is a bounded, penetrable and possibly…

Numerical Analysis · Mathematics 2025-05-15 Peter Monk , Manuel Pena , Virginia Selgas

The Helmholtz equation with variable wavenumbers is challenging to solve numerically due to the pollution effect, which often results in a huge ill-conditioned linear system. In this paper, we present a high-order wavelet Galerkin method to…

Numerical Analysis · Mathematics 2025-03-25 Bin Han , Michelle Michelle

Passive imaging involves recording waves generated by uncontrolled, random sources and utilizing correlations of such waves to image the medium through which they propagate. In this paper, we focus on passive inverse obstacle scattering…

Analysis of PDEs · Mathematics 2025-11-06 Thorsten Hohage , Meng Liu

A low frequency approximation of the discrete Sommerfeld diffraction problems, involving the scattering of a time harmonic lattice wave incident on square lattice by a discrete Dirichlet or a discrete Neumann half-plane, is investigated. It…

Analysis of PDEs · Mathematics 2019-08-08 Basant Lal Sharma