Abstract
The usual time domain Boundary Element Method (BEM) contains fundamentalsolutions which are convoluted with time-dependent boundary data andintegrated over the boundary surface. Here, a new approach for theevaluation of the convolution integrals, the so-called ’OperationalQuadrature Methods‘ developed by Lubich, is presented. In thisformulation, the convolution integral is numerically approximated by aquadrature formula whose weights are determined using the Laplacetransform of the fundamental solution and a linear multisep method. Tostudy the behaviour of the method, the numerical convolution of afundamental solution with a unit step function is compared with theanalytical result. Then, a time domain Boundary Element formulationapplying the ’Operational Quadrature Methods‘ is derived. For thisformulation only the fundamental solutions in Laplace domain arenecessary. The properties of the new formulation are studied with anumerical example.
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SCHANZ, M., ANTES, H. Application of ‘Operational Quadrature Methods’ in Time Domain Boundary Element Methods. Meccanica 32, 179–186 (1997). https://doi.org/10.1023/A:1004258205435
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DOI: https://doi.org/10.1023/A:1004258205435