The International Conference for High Performance Computing, Networking, Storage and Analysis
A Scalable Schwarz Method for 3D Linear Elasticity Problems on Domains with Complex Geometry.
Authors: Fande Kong (University of Colorado Boulder), Xiao-Chuan Cai (University of Colorado Boulder)
Abstract: Several iterative algorithms for solving the elasticity equation are theoretically scalable in the sense that the number of iterations doesn't grow much when the number of processors is increased. However, the theoretically optimal scalability doesn't translate into linear scalability in total compute time, especially when the number of processors is large, because the coarse level solvers aren't scalable in terms of the compute time. We introduce a new way to construct coarse level spaces that preserve the geometric features of the computational domain, but give up accuracy in the interior of the domain. As it turns out the tradeoff in accuracy provides the high scalability in terms of the total compute time. We show numerically that such a new preconditioner is highly scalable for solving linear elasticity equation discretized on unstructured 3D meshes with hundreds of millions of unknowns on a supercomputer with over 10,000 processors.