An MSSS-preconditioned matrix equation approach for the time-harmonic elastic wave equation at multiple frequencies

Journal article (2018)

Authors

M.M. Baumann Numerical Analysis - EEMCS
R.A. Astudillo Rengifo Numerical Analysis - EEMCS
Y. Qiu Max Planck Institute for Dynamics of Complex Technical Systems
Y.M.E. Ang Nanyang Technological University
M.B. van Gijzen Numerical Analysis - EEMCS
RE Plessix Shell Global Solutions International B.V.
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2018 M.M. Baumann, R.A. Astudillo Rengifo, Y. Qiu, Y.M.E. Ang, M.B. van Gijzen, R.E. Plessix
DOI
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https://doi.org/10.1007/s10596-017-9667-7
Time-harmonic elastic wave equation Induced dimension reduction (IDR) method Multilevel sequentially semiseparable (MSSS) matrices Multiple frequencies Preconditioned matrix equations
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Published Date

2018

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

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.