TY - JOUR

T1 - An MSSS-preconditioned matrix equation approach for the time-harmonic elastic wave equation at multiple frequencies

AU - Baumann, M.

AU - Astudillo, R.

AU - Qiu, Y.

AU - Ang, E.Y.M.

AU - van Gijzen, M.B.

AU - Plessix, R.E.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Induced dimension reduction (IDR) method

KW - Multilevel sequentially semiseparable (MSSS) matrices

KW - Multiple frequencies

KW - Preconditioned matrix equations

KW - Time-harmonic elastic wave equation

UR - http://resolver.tudelft.nl/uuid:ed57b9db-66b1-44f9-9903-9cd12b49b17c

UR - http://www.scopus.com/inward/record.url?scp=85021073538&partnerID=8YFLogxK

U2 - 10.1007/s10596-017-9667-7

DO - 10.1007/s10596-017-9667-7

M3 - Article

AN - SCOPUS:85021073538

VL - 22

SP - 43

EP - 61

JO - Computational Geosciences: modeling, simulation and data analysis

JF - Computational Geosciences: modeling, simulation and data analysis

SN - 1420-0597

IS - 1

ER -