TIME DOMAIN BOUNDARY ELEMENT METHODS FOR THE NEUMANN PROBLEM： ERROR ESTIMATES AND ACOUSTIC PROBLEMS

We investigate time domain boundary element methods for the wave equation in R3, with a view towards sound emission problems in computational acoustics. The Neumann problem is reduced to a time dependent integral equation for the hypersingular operator, and we present a priori and a posteriori error...

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Bibliographic Details
Published inJournal of computational mathematics Vol. 36; no. 1; pp. 70 - 89
Main Authors Gimperlein, Heiko, Özdemir, Ceyhun, Stephan, Ernst P.
Format Journal Article
LanguageEnglish
Published Chinese Academy of Mathematices and Systems Science (AMSS) Chinese Academy of Sciences 01.01.2018
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Summary:We investigate time domain boundary element methods for the wave equation in R3, with a view towards sound emission problems in computational acoustics. The Neumann problem is reduced to a time dependent integral equation for the hypersingular operator, and we present a priori and a posteriori error estimates for conforming Galerkin approxima- tions in the more general case of a screen. Numerical experiments validate the convergence of our boundary element scheme and compare it with the numerical approximations ob- tained from an integral equation of the second kind. Computations in a half-space illustrate the influence of the reflection properties of a flat street.
Bibliography:Time domain boundary element method, Wave equation, Neumann problem,Error estimates, Sound radiation.
We investigate time domain boundary element methods for the wave equation in R3, with a view towards sound emission problems in computational acoustics. The Neumann problem is reduced to a time dependent integral equation for the hypersingular operator, and we present a priori and a posteriori error estimates for conforming Galerkin approxima- tions in the more general case of a screen. Numerical experiments validate the convergence of our boundary element scheme and compare it with the numerical approximations ob- tained from an integral equation of the second kind. Computations in a half-space illustrate the influence of the reflection properties of a flat street.
11-2126/O1
ISSN:0254-9409
1991-7139
DOI:10.4208/jcm.1610-m2016-0494