Investigating Schwarz domain decomposition based preconditioners for efficient geophysical electromagnetic field simulation

Kary, Benjamin R. (2017) Investigating Schwarz domain decomposition based preconditioners for efficient geophysical electromagnetic field simulation. Masters thesis, Memorial University of Newfoundland.

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Abstract

In this thesis, I researched and implemented a number of Schwarz domain decomposition algorithms with the intent of finding an efficient method to solve the geophysical EM problem. I began by using finite difference and finite element discretizations to investigate the domain decomposition algorithms for the Poisson problem. I found that the Schwarz methods were best used as a preconditioner to a Krylov iteration. The optimized Schwarz (OS) preconditioner outperformed the related restricted additive Schwarz (RAS) preconditioner and both of the local and global OS fixed point iterations. Using finite differences the OS preconditioner performed much better than the RAS preconditioner, but using finite element in parallel with the FEniCS assembly library, their performance was similar. The FEniCS library automatically partitions the global mesh into subdomains and produces irregular partition boundaries. By creating a serial rectangular subdomain code in FEniCS, I regained the benefit of the OS preconditioner, suggesting that the irregular partitioning scheme was detrimental to the convergence behaviour of the OS preconditioner. Based on my work for the Poisson problem, I decided to attempt both a RAS and OS preconditioned GMRES iteration for the electromagnetic problem. Due to the unstructured meshes and source/receiver refinement used in EM modelling I could not avoid the irregular mesh partitioning, and the OS preconditioner lagged the RAS preconditioner in terms of iteration count. On the bright side, the RAS preconditioner worked very well, and outperformed any of the preconditioners bundled with PETSc in terms of both iteration count and time to solution.

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