Iterative Solution of Singular Systems with Applications

摘要

This paper deals with efficient solution of singular symmetric positive semidefinite problems. Our motivation arises from the need to solve special problems of geotechnics, e.g. to perform upscaling analysis of geocomposites. In that and other applications we have to solve boundary problems with pure Neumann boundary conditions. We show that the stabilized PCG method with various preconditioners is a good choice for systems resulting from the numerical solution of Neumann problems, or more generally problems with a known small dimensional null space. We make use of this scenario to compare parallel implementations of the corresponding solvers, namely implementations in the in-house finite element software GEM and implementations employing components of the general Trilinos framework. The studies show that the solvers based on GEM are highly competitive with its recognized counterpart.