A Fast Iterative Solution of the Time-harmonic Wave Equation with MSSS-preconditioned IDR(s)
M. Baumann and M.B. Van Gijzen
Event name: 78th EAGE Conference and Exhibition 2016 - Workshops
Session: WS13-Methods and Challenges of Seismic Wave Modelling for Seismic Imaging
Publication date: 31 May 2016
Info: Extended abstract, PDF ( 1.87Mb )
Price: € 20
For the Full Waveform Inversion in frequency-domain, the fast numerical solution of the time-harmonic wave equation is required. For large three-dimensional problems, the problem size exceeds several million of unknowns, and a short-recurrence Krylov method such as IDR(s) is used to solve linear systems of this size. Especially for high-frequency simulations, an efficient preconditioner needs to be applied in order to speed-up convergence. In our presentation, we introduce a new preconditioner for the time-harmonic wave equation that exploits the hierarchical structure of the discretized problem. We use multilevel sequentially semiseparable (MSSS) matrix computations for the approximate inversion of the preconditioner. For large three-dimensional problems, we present a memory-efficient modification of the MSSS preconditioner that resembles the approximate solution of a sequence of two-dimensional problems. We conclude our presentation with numerical examples for the time-harmonic wave equation in both acoustic and elastic media, and in two and three spatial dimensions.