Abstract
In this work, we present a new numerical framework for the efficient solution of the time-harmonic elastic wave equation at multiple frequencies. We show that multiple frequencies (and multiple right-hand sides) can be incorporated when the discretized problem is written as a matrix equation. This matrix equation can be solved efficiently using the preconditioned IDR(s) method. We present an efficient and robust way to apply a single preconditioner using MSSS matrix computations. For 3D problems, we present a memory-efficient implementation that exploits the solution of a sequence of 2D problems. Realistic examples in two and three spatial dimensions demonstrate the performance of the new algorithm.
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Acknowledgments
We would like to thank Joost van Zwieten, co-developer of the open source project nutils Footnote 1 for helpful discussions concerning the finite element discretization described in Section 2.2. Shell Global Solutions International B.V. is gratefully acknowledged for financial support of the first author.
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Baumann, M., Astudillo, R., Qiu, Y. et al. An MSSS-preconditioned matrix equation approach for the time-harmonic elastic wave equation at multiple frequencies. Comput Geosci 22, 43–61 (2018). https://doi.org/10.1007/s10596-017-9667-7
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DOI: https://doi.org/10.1007/s10596-017-9667-7