Optimization of direct domain decomposition methods

Abstract

In this paper, the problem of parallelizing the finite element method for distributed memory computers using domain decomposition methods is addressed. We focus on direct domain decomposition methods because they are robust and well adapted to multi-level decompositions. Two important problems concerning these methods are studied: the condensation of subdomains and the resolution of the interface problem. Finally, results are presented which show that, in sequential implementation, direct domain decomposition methods are more efficient than standard LDL^t-skyline solvers, and compare favorably with state-of-the-art LDL^t-sparse solvers.