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This article proposes a boundary element method for the dynamic contact between a linearly elastic body and a rigid obstacle. The Signorini contact problem is formulated as a variational inequality for the Poincar\'{e}-Steklov operator for…

Numerical Analysis · Mathematics 2023-08-08 Alessandra Aimi , Giulia Di Credico , Heiko Gimperlein

In this paper, we consider a variational formulation for the Dirichlet problem of the wave equation with zero boundary and initial conditions, where we use integration by parts in space and time. To prove unique solvability in a subspace of…

Numerical Analysis · Mathematics 2021-01-19 Olaf Steinbach , Marco Zank

Solutions to the wave equation in the exterior of a polyhedral domain or a screen in $\mathbb{R}^3$ exhibit singular behavior from the edges and corners. We present quasi-optimal $hp$-explicit estimates for the approximation of the…

Numerical Analysis · Mathematics 2020-03-06 Heiko Gimperlein , Ceyhun Oezdemir , David Stark , Ernst P. Stephan

The solution of the wave equation in a polyhedral domain in $\mathbb{R}^3$ admits an asymptotic singular expansion in a neighborhood of the corners and edges. In this article we formulate boundary and screen problems for the wave equation…

Numerical Analysis · Mathematics 2018-07-17 Heiko Gimperlein , Fabian Meyer , Ceyhun Oezdemir , David Stark , Ernst P. Stephan

This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded $d$-dimensional domain. First, an explicit reconstruction formula for the density is established by means of the…

Analysis of PDEs · Mathematics 2023-01-20 Bochao Chen , Yixian Gao , Shuguan Ji , Yang Liu

This article studies a boundary element method for dynamic frictional contact between linearly elastic bodies. We formulate these problems as a variational inequality on the boundary, involving the elastodynamic Poincar\'{e}-Steklov…

Numerical Analysis · Mathematics 2024-05-27 Alessandra Aimi , Giulia Di Credico , Heiko Gimperlein

This paper is concerned with the study of the well-posedeness for the initial boundary value problem to the time-fractional wave equation with acoustic boundary conditions. The problem is considered in a bounded and connected domain $\Omega…

Analysis of PDEs · Mathematics 2023-09-25 Paulo M. de Carvalho-Neto , Cícero L. Frota , Pedro G. P. Torelli

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

In this paper, we consider numerical solutions of a time domain acoustic-elastic wave interaction problem which occurs between a bounded penetrable elastic body and a compressible inviscid fluid. It is also called the fluid-solid…

Numerical Analysis · Mathematics 2019-03-20 Yingda Cheng , Jing Huang , Xiaozhou Li , Liwei Xu

This article investigates adaptive mesh refinement procedures for the time-domain wave equation with Neumann boundary conditions, formulated as an equivalent hypersingular boundary integral equation. Space-adaptive and time-adaptive…

Numerical Analysis · Mathematics 2025-08-28 Alessandra Aimi , Giulia Di Credico , Heiko Gimperlein , Chiara Guardasoni

In this paper, we consider an acoustic wave transmission problem with mixed boundary conditions of Dirichlet, Neumann, and impedance type. The transmission interfaces may join the domain boundary in a general way independent of the location…

Numerical Analysis · Mathematics 2020-10-07 Sarah Eberle , Francesco Florian , Ralf Hiptmair , Stefan A. Sauter

In this paper, we recast the variational formulation corresponding to the single layer boundary integral operator $\operatorname{V}$ for the wave equation as a minimization problem in $L^2(\Sigma)$, where $\Sigma := \partial \Omega \times…

Numerical Analysis · Mathematics 2023-12-21 Daniel Hoonhout , Richard Löscher , Olaf Steinbach , Carolina Urzúa-Torres

Given the wave equation on a compact Riemannian manifold with boundary, we derive an explicit reconstruction procedure to represent the frequency-domain Neumann-to-Dirichlet map in terms of the time-domain Neumann-to-Dirichlet map at any…

Analysis of PDEs · Mathematics 2026-02-17 Yang Yang

We present a novel analysis of the boundary integral operators associated to the wave equation. The analysis is done entirely in the time-domain by employing tools from abstract evolution equations in Hilbert spaces and semi-group theory.…

Numerical Analysis · Mathematics 2018-04-23 Matthew Hassell , Tianyu Qiu , Tonatiuh Sanchez-Vizuet , Francisco-Javier Sayas

It is well known that the Fourier series Dirichlet-to-Neumann (DtN) boundary condition can be used to solve the Helmholtz equation in unbounded domains. In this work, applying such DtN boundary condition and using the finite element method,…

Numerical Analysis · Mathematics 2019-02-12 Liwei Xu , Tao Yin

Consider the scattering of a time-harmonic elastic plane wave by a bi-periodic rigid surface. The displacement of elastic wave motion is modeled by the three-dimensional Navier equation in an open domain above the surface. Based on the…

Numerical Analysis · Mathematics 2020-07-28 Gang Bao , Xue Jiang , Peijun Li , Xiaokai Yuan

This paper presents a combined field and boundary integral equation method for solving the time-dependent scattering problem of a thermoelastic body immersed in a compressible, inviscid and homogeneous fluid. The approach here is a…

Numerical Analysis · Mathematics 2018-04-23 George Hsiao , Tonatiuh Sanchez-Vizuet , Francisco-Javier Sayas , Richard Weinacht

We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the…

Numerical Analysis · Mathematics 2025-05-20 Tonatiuh Sánchez-Vizuet

We study the wave equation in a bounded domain or on a compact Riemannian manifold with boundary. Assume that we are given the hyperbolic Neumann-to-Dirichlet map on the boundary corresponding to physical boundary measurements. We consider…

Analysis of PDEs · Mathematics 2007-08-17 Matias Dahl , Anna Kirpichnikova , Matti Lassas

We show existence and uniqueness for a linearized water wave problem in a two dimensional domain $G$ with corner, formed by two semi-axis $\Gamma_1$ and $\Gamma_2$ which intersect under an angle $\alpha\in (0,\pi ]$. The existence and…

Analysis of PDEs · Mathematics 2010-05-20 Calin Iulian Martin
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