The solution of the wave equation in a polyhedral domain admits an
asymptotic expansion in a neighborhood of the corners and edges.
In this article we formulate boundary and screen problems for the
wave equation as an equivalent boundary integral equations in time
domain and study the regularity properties and numerical approximation
of the solution. Guided by the theory for elliptic equations, graded
meshes are shown to recover the optimal approximation rates expected
for smooth solutions. Numerical experiments illustrate the theory
for screen problems. In particular, we discuss the Dirichlet problem,
the Dirichlet-to-Neumann operator and applications to the sound emitted
by a tire.
%0 Journal Article
%1 gimperlein2018boundary
%A Gimperlein, Heiko
%A Meyer, Fabian
%A Özdemir, Ceyhun
%A Stark, David
%A Stephan, Ernst P.
%D 2018
%K ians imported
%N 4
%P 867–912
%T Boundary elements with mesh refinements for the wave equation
%V 39
%X The solution of the wave equation in a polyhedral domain admits an
asymptotic expansion in a neighborhood of the corners and edges.
In this article we formulate boundary and screen problems for the
wave equation as an equivalent boundary integral equations in time
domain and study the regularity properties and numerical approximation
of the solution. Guided by the theory for elliptic equations, graded
meshes are shown to recover the optimal approximation rates expected
for smooth solutions. Numerical experiments illustrate the theory
for screen problems. In particular, we discuss the Dirichlet problem,
the Dirichlet-to-Neumann operator and applications to the sound emitted
by a tire.
@article{gimperlein2018boundary,
abstract = {The solution of the wave equation in a polyhedral domain admits an
asymptotic expansion in a neighborhood of the corners and edges.
In this article we formulate boundary and screen problems for the
wave equation as an equivalent boundary integral equations in time
domain and study the regularity properties and numerical approximation
of the solution. Guided by the theory for elliptic equations, graded
meshes are shown to recover the optimal approximation rates expected
for smooth solutions. Numerical experiments illustrate the theory
for screen problems. In particular, we discuss the Dirichlet problem,
the Dirichlet-to-Neumann operator and applications to the sound emitted
by a tire.},
added-at = {2019-06-17T14:25:24.000+0200},
author = {Gimperlein, Heiko and Meyer, Fabian and Özdemir, Ceyhun and Stark, David and Stephan, Ernst P.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2f77926753a45199c67dd623a73f628f6/britsteiner},
interhash = {66294e795d83a31ff42ca7e988189c75},
intrahash = {f77926753a45199c67dd623a73f628f6},
journaltitle = {Numerische Mathematik},
keywords = {ians imported},
language = {eng},
number = 4,
pages = {867–912},
timestamp = {2019-06-17T12:34:15.000+0200},
title = {Boundary elements with mesh refinements for the wave equation},
volume = 39,
year = 2018
}