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

Solving large sparse linear systems in 3-D 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 multi-source problems. Popular scientific tools for solving a linear system like MUMPS, STRUMPACK, and PETSc can be utilized, but their applicability to our specific problem has not been comprehensively evaluated. Our study aims at tackling the challenges in solving large sparse, complex-valued symmetric linear systems with multiple right-hand-side vectors for 3-D frequency-domain seismic wave modeling. We have leveraged preconditioned conjugate gradient iterative algorithms as the foundation for our research, introducing two highly cost-effective parallel iterative solvers: the Parallel Symmetric Successive Over-Relaxation Conjugate Gradient (P-SSORCG) and the Parallel Incomplete Cholesky Conjugate Gradient (P-ICCG). These novel solvers were subjected to a comprehensive comparative analysis against well-established scientific tools, including MUMPS, STRUMPACK, and PETSc, in the context of 3-D frequency-domain seismic wave modeling. We show their promising performances in a practical 3-D SEG/EAGE overthrust model and demonstrate that the grouped P-SSORCG offers an efficient alternative to parallel direct solvers, particularly in situations where computational resources are limited.