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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Published in | Journal of computational mathematics Vol. 36; no. 1; pp. 70 - 89 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Chinese Academy of Mathematices and Systems Science (AMSS) Chinese Academy of Sciences
01.01.2018
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Online Access | Get full text |
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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. |
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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 |