A Robust Parallel Iterative Solver for Frequency-domain Elastic Wave Modeling

Abstract

Frequency-domain elastic wave modeling relies on an efficient linear solver for the large, sparse, ill-conditioned linear system derived from the discretization of the elastic wave equation. Direct solvers are mostly based on LU decomposition. These methods are efficient for multiple right-hand sides problems, but they require significant memory resources. Conversely, iterative solvers benefit from the sparsity of the system, but they require sophisticated preconditioners to converge due to the system ill-conditioning. In this study, we investigate the performance of an iterative method named CARP-CG for frequency-domain elastic wave modeling. The CARP-CG method transforms the original system into a symmetric positive semi-definite system by cyclic row-projections. This system is efficiently solved with the conjugate gradient (CG) method. The cyclic row-projection transformation can be seen as a purely algebraic preconditioning technique which is easy to implement. The algorithm can be parallelized through a row-block decomposition combined with component-averaging operations. Numerical experiments on the 2D frequency-domain elastic problem with high Poisson's ratio exhibit a good scalability of CARP-CG. Comparisons for different frequencies between CARP-CG and standard Krylov iterative solvers (GMRES and CG on the normal equations) emphasize the robustness and the fast convergence of the method.