3-D parallel frequency-domain visco-acoustic wave modelling based on a hybrid direct/iterative solver

摘要

We present a parallel domain decomposition method based on a hybrid direct-iterative solver for 3D frequency-domain modelling of visco-acoustic waves. Frequency-domain seismic modelling reduces to the solution of a large and sparse system of linear equations for each frequency. The hybrid direct-iterative approach aims to overcome the memory requirement and the limited scalability of direct-solver approaches, on the one hand, and to iteratively solve better-conditioned system than in global iterative approaches on the other hand. The domain decomposition is based upon the algebraic Schur complement method. The reduced Schur complement system is solved with the global minimum residual method (GMRES) and is preconditioned by an algebraic additive Schwarz preconditioner. The MUMPS direct solver is used to factorize local impedance matrices defined on each subdomain. Simulations in the salt models for frequencies up to 12.5 Hz show that the number of iterations increases linearly with frequencies when the grid interval is matched to the frequency and the size of the subdomains is kept constant over frequencies. This makes the time complexity of the hybrid approach similar to that of global iterative solvers. Possible improvements of the method for multi-source simulation involve the use of block iterative solver and two levels of parallelism.