On cost-efficient parallel iterative solvers for 3D frequency-domain seismic multisource viscoelastic anisotropic wave modeling

Abstract

Solving large sparse linear systems in 3D frequency-domain seismic wave modeling, especially in viscoelastic anisotropic media, poses significant challenges due to the increasing number of discrete moduli and nonzero elements in the linear system matrix. The computational load surpasses that of acoustic or viscoacoustic media, making it even more challenging when dealing with multisource problems. Popular scientific tools for solving a linear system, such as multifrontal massively parallel sparse direct solver (MUMPS), structured matrix package (STRUMPACK), and portable extensible toolkit for scientific computation (PETSc), can be used, but their applicability to our specific problem has not been comprehensively evaluated. Our study aims to tackle the challenges in solving large, sparse, complex-valued symmetric linear systems with multiple right-hand side vectors for 3D frequency-domain seismic wave modeling. We have adopted the preconditioned conjugate gradient iterative algorithms as the foundation for our research, introducing two highly cost-effective parallel iterative solvers: the parallel symmetric successive overrelaxation conjugate gradient (P-SSORCG) and the parallel incomplete Cholesky conjugate gradient (P-ICCG). These novel solvers are subjected to a comprehensive comparative analysis against well-established scientific tools, such as MUMPS, STRUMPACK, and PETSc, in the context of 3D frequency-domain seismic wave modeling. We show their promising performances in a practical 3D SEG/EAGE overthrust model and demonstrate that the grouped P-SSORCG offers an efficient alternative to parallel direct solvers, particularly in situations wherein computational resources are limited.