An MSSS-preconditioned matrix equation approach for the time-harmonic elastic wave equation at multiple frequencies
M. Baumann (TU Delft - Electrical Engineering, Mathematics and Computer Science)
R. Astudillo (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Y. Qiu (Max Planck Institute for Dynamics of Complex Technical Systems)
E.Y.M. Ang (Nanyang Technological University)
M.B. van Gijzen (TU Delft - Electrical Engineering, Mathematics and Computer Science)
R.E. Plessix (Shell Global Solutions International B.V.)
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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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