Abstract
We investigate the numerical performance of an iterative solver for a frequency-domain finite-difference discretization of the isotropic elastic wave equation. The solver is based on the ‘shifted-Laplacian’ preconditioner, originally designed for the acoustic wave equation. This preconditioner represents a discretization of a heavily damped wave equation and can be efficiently inverted by a multigrid iteration. However, the application of multigrid to the elastic case is not straightforward because standard methods, such as point-Jacobi, fail to smooth the S-wave wavenumber components of the error when high P-to-S velocity ratios are present. We consider line smoothers as an alternative and apply local-mode analysis to evaluate the performance of the various components of the multigrid preconditioner. Numerical examples in 2-D demonstrate the efficacy of our method.
Original language | English |
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Pages (from-to) | 47-65 |
Number of pages | 19 |
Journal | Journal of Computational Physics |
Volume | 317 |
Issue number | July |
DOIs | |
Publication status | Published - 27 Apr 2016 |
Keywords
- Multigrid
- Elastic
- Wave equation
- Frequency domain
- Finite-difference