hp-version time domain boundary elements for the wave equation on quasi-uniform meshes

Heiko Gimperlein; Ceyhun Özdemir; David Stark; Ernst P. Stephan

doi:10.1016/j.cma.2019.07.018

hp-version time domain boundary elements for the wave equation on quasi-uniform meshes

Heiko Gimperlein, Ceyhun Özdemir, David Stark, Ernst P. Stephan

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Abstract

Solutions to the wave equation in the exterior of a polyhedral domain or a screen in R3 exhibit singular behavior from the edges and corners. We present quasi-optimal hp-explicit estimates for the approximation of the Dirichlet and Neumann traces of these solutions for uniform time steps and (globally) quasi-uniform meshes on the boundary. The results are applied to an hp-version of the time domain boundary element method. Numerical examples confirm the theoretical results for the Dirichlet problem both for screens and polyhedral domains.

Original language	English
Pages (from-to)	145-174
Number of pages	30
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	356
Early online date	23 Jul 2019
DOIs	https://doi.org/10.1016/j.cma.2019.07.018
Publication status	Published - 1 Nov 2019

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https://arxiv.org/pdf/1811.01595.pdf

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title = "hp-version time domain boundary elements for the wave equation on quasi-uniform meshes",

abstract = "Solutions to the wave equation in the exterior of a polyhedral domain or a screen in R3 exhibit singular behavior from the edges and corners. We present quasi-optimal hp-explicit estimates for the approximation of the Dirichlet and Neumann traces of these solutions for uniform time steps and (globally) quasi-uniform meshes on the boundary. The results are applied to an hp-version of the time domain boundary element method. Numerical examples confirm the theoretical results for the Dirichlet problem both for screens and polyhedral domains.",

author = "Heiko Gimperlein and Ceyhun {\"O}zdemir and David Stark and Stephan, {Ernst P.}",

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AU - Gimperlein, Heiko

AU - Özdemir, Ceyhun

AU - Stark, David

AU - Stephan, Ernst P.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - Solutions to the wave equation in the exterior of a polyhedral domain or a screen in R3 exhibit singular behavior from the edges and corners. We present quasi-optimal hp-explicit estimates for the approximation of the Dirichlet and Neumann traces of these solutions for uniform time steps and (globally) quasi-uniform meshes on the boundary. The results are applied to an hp-version of the time domain boundary element method. Numerical examples confirm the theoretical results for the Dirichlet problem both for screens and polyhedral domains.

AB - Solutions to the wave equation in the exterior of a polyhedral domain or a screen in R3 exhibit singular behavior from the edges and corners. We present quasi-optimal hp-explicit estimates for the approximation of the Dirichlet and Neumann traces of these solutions for uniform time steps and (globally) quasi-uniform meshes on the boundary. The results are applied to an hp-version of the time domain boundary element method. Numerical examples confirm the theoretical results for the Dirichlet problem both for screens and polyhedral domains.

U2 - 10.1016/j.cma.2019.07.018

DO - 10.1016/j.cma.2019.07.018

M3 - Article

VL - 356

SP - 145

EP - 174

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -

hp-version time domain boundary elements for the wave equation on quasi-uniform meshes

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