Mesh partitioning for implicit computations via iterative domain decomposition: Impact and optimization of the subdomain aspect ratio

Abstract

AbstractOptimal domain decomposition methods have emerged as powerful iterative algorithms for parallel implicit computations. Their key preprocessing step is mesh partitioning, where research has focused so far on the automatic generation of load‐balanced subdomains with minimum interface nodes. In this paper, we emphasize the importance of the subdomain aspect ratio as a mesh partitioning factor, and highlight its impact on the convergence rate of an optimal domain decomposition based iterative method. We also present a fast optimization algorithm for improving the aspect ratio of existing mesh partitions, and illustrate it with several examples from fluid dynamics and structural mechanics applications. For a stiffened shell problem decomposed by the optimal Recursive Spectral Bisection scheme and solved by the FETI method, this optimization algorithm is shown to improve the solution time by a factor equal to 1·54 and to restore numerical scalability.