Cost-effective parallel iterative methods

What is it about?

In 3-D seismic wave modeling, especially in complex viscoelastic anisotropic environments, solving large sparse linear systems poses significant challenges. These challenges arise due to the increasing complexity of the system matrix, which contains numerous discrete moduli and nonzero elements. This complexity leads to a computational burden that exceeds that of simpler media types like acoustic or viscoacoustic, particularly when dealing with multi-source scenarios. Commonly used scientific tools for solving linear systems, such as MUMPS, STRUMPACK, and PETSc, are available, but their suitability for our specific problem has not been thoroughly assessed. Our research addresses this gap by focusing on solving large sparse, complex-valued symmetric linear systems with multiple right-hand-side vectors for 3-D frequency-domain seismic wave modeling. In addition, we have employed preconditioned conjugate gradient iterative algorithms as the basis of our study. We have developed two new highly efficient parallel iterative solvers: the Parallel Symmetric Successive Over-Relaxation Conjugate Gradient (P-SSORCG) and the Parallel Incomplete Cholesky Conjugate Gradient (P-ICCG). These solvers have undergone a comprehensive comparative analysis against established scientific tools like MUMPS, STRUMPACK, and PETSc within the context of 3D frequency-domain seismic wave modeling.

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Why is it important?

Our results demonstrate the promising performance of these novel solvers, particularly in practical applications such as a 3-D SEG/EAGE overthrust model. Notably, the grouped P-SSORCG solver presents an efficient alternative to parallel direct solvers, especially in scenarios where computational resources are limited.