A Galerkin method for retarded boundary integral equations with smooth and compactly supported temporal basis functions
type: Item
instance of: scholarly article
title: A Galerkin method for retarded boundary integral equations with smooth and compactly supported temporal basis functions
zbMATH Open document ID: 1262.65125
author: Alexander Veit
author: S. Sauter
published in: Numerische Mathematik
publication date: 2013-02-25T00:00:00Z
full work available at URL: ZORA NL 87098.pdf
review text: The authors present a new time discretization method for retarded potential equations which circumvents numerical integration over intersections of the light cone with the spatial surface mesh. The method is tested on the wave equation on a sphere with Dirichlet boundary conditions on the boundary \(\Gamma\). They employ an ansatz as a single layer potential for the solution \(u\) of the wave equation: \[ u(x, t) := S\phi(x, t) :=\int_\Gamma \frac{\phi(y, t-\|x-y\|)}{4\pi\|x-y\|}\,d\Gamma_y, \] for \((x, t) \in \Omega\times[0,T]\), with unknown density function \(\phi\). The ansatz satisfies the wave equation and the initial conditions. Since the single layer potential can be extended continuously to the boundary \(\Gamma\), the unknown density function \(\phi\) is determined such that the boundary conditions \(u=g\) on \(\Gamma\times[0,T]\) are satisfied. This results in the boundary integral equation for \(\phi\), \(S\phi(x,t)=g(x,t)\) for all \((x,t)\in \Gamma\times[0,T]\), which is solved numerically by a space-time variational formulation.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 65M38
Mathematics Subject Classification ID: 35L05
zbMATH DE Number: 6138628
zbMATH Keywords: Galerkin method
zbMATH Keywords: retarded boundary integral equation
zbMATH Keywords: variable time stepping
zbMATH Keywords: variable order
zbMATH Keywords: wave equation
describes a project that uses: Matlab
MaRDI profile type: Publication
OpenAlex ID: W2030031881
cites work: Q3331506
cites work: THE PARTITION OF UNITY METHOD
cites work: Formulation variationnelle espace‐temps pour le calcul par potentiel retardé de la diffraction d'une onde acoustique (I)
cites work: Multistep and Multistage Convolution Quadrature for the Wave Equation: Algorithms and Experiments
cites work: Runge-Kutta convolution quadrature for operators arising in wave propagation
cites work: Rapid Solution of the Wave Equation in Unbounded Domains
cites work: Wave Propagation Problems Treated with Convolution Quadrature and BEM
cites work: Elastodynamic direct boundary element methods with enhanced numerical stability properties
cites work: ANALYSIS OF THREE-DIMENSIONAL TRANSIENT ACOUSTIC WAVE PROPAGATION USING THE BOUNDARY INTEGRAL EQUATION METHOD
cites work: Analysis of Convolution Quadrature Applied to the Time-Domain Electric Field Integral Equation
cites work: Exponential convergence of {\(hp\)} quadrature for integral operators with Gevrey kernels
cites work: Averaging techniques for time-marching schemes for retarded potential integral equations
cites work: Q4424582
cites work: Q4275389
cites work: Q4450077
cites work: A Galerkin BEM for transient acoustic scattering by an absorbing obstacle
cites work: Sparse Convolution Quadrature for Time Domain Boundary Integral Formulations of the Wave Equation by Cutoff and Panel-Clustering
cites work: Sparse convolution quadrature for time domain boundary integral formulations of the wave equation
cites work: Boundary Element Methods
cites work: New explicit formulas for the \(n\)th derivative of composite functions
cites work: Is Gauss Quadrature Better than Clenshaw–Curtis?
cites work: A Finite Difference Delay Modeling Approach to the Discretization of the Time Domain Integral Equations of Electromagnetics
cites work: Q4517879
cites work: An Accurate Scheme for the Solution of the Time-Domain Integral Equations of Electromagnetics Using Higher Order Vector Bases and Bandlimited Extrapolation
DOI: 10.1007/S00211-012-0483-7
description: scientific article; zbMATH DE number 6138628