CARP-CG: A robust parallel iterative solver for frequency-domain elastic wave modeling, application to the Marmousi2 model
Résumé
Solving the frequency-domain elastic wave equations relies on an efficient linear solver for the large, sparse, indefinite and ill-conditioned linear system derived from the discretization of the elastic wave equation. Direct solvers, which are mostly based on LU decomposition, are efficient for multiple right-hand sides problems, but the memory requirement is huge due to the fill-in effects. On the contrary, iterative solvers fully benefit from the sparsity of the system, but they require problem-specific preconditioners to ensure the convergence because of the ill-conditioning of the system. In this study, we investigate the performance of a robust iterative method named CARP-CG for frequency-domain elastic wave modeling. CARP-CG method turns the original system into a symmetric positive semi-definite system by Kaczmarz row-projections. Such a system can be efficiently solved by the conjugate gradient (CG) method. The row-projections can be seen as a purely algebraic preconditioning technique which is general and is easy to implement. The parallelization is straightforward through a row-block decomposition combined with a component-averaging method. We discretize the 2D frequency-domain elastic wave equation through a 4th order finite difference scheme. Numerical experiments on the Marmousi2 model exhibit a good scalability of CARP-CG. Comparisons between CARP-CG and standard Krylov iterative solvers (GMRES and CGNR) further emphasize the robustness and the fast convergence of CARP-CG method.