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Time Domain BIEM with CQM Accelerated with ACA and Truncation for the Wave Equation

H. Yoshikawa1, R. Matsuura2, N. Nishimura1
Kyoto University, Kyoto, Japan.
NTT R& D, Japan.

Computer Modeling in Engineering & Sciences 2013, 94(6), 553-565.


The convolution integrals with respect to time in the time domain boundary integral equation method (TD-BIEM) are calculated approximately using the Lubich convolution quadrature method (CQM). The influence matrices in the discretized boundary integral equation are computed with the Laplace transform of the fundamental solution in TD-BIEM with the Lubich CQM. These matrices, however, are dense, and both the computational cost and memory requirements are high. In this paper, we apply Adaptive Cross Approximation (ACA) to the influence matrices to achieve a fast solver of TD-BIEM with the Lubich CQM. Moreover, we reduce the computational time of TD-BIEM with the Lubich CQM for hyperbolic PDE problems considering the arrival time of the influence from the source element to the observation point and using cast forward idea. The effect of the proposed method is confirmed with some numerical results.


time domain BIEM, CQM, ACA, truncation, cast forward

Cite This Article

Yoshikawa, H., Matsuura, R., Nishimura, N. (2013). Time Domain BIEM with CQM Accelerated with ACA and Truncation for the Wave Equation. CMES-Computer Modeling in Engineering & Sciences, 94(6), 553–565.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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