A parallel linear solver exploiting the physical properties of the underlying mechanical problem

Abstract

The iterative solution of large systems of equations may benefit from parallel processing. However, using a straight-forward domain decomposition in “layered” geomechanical finite element models with significantly different stiffnesses may lead to slow or non-converging solutions. Physics-based domain decomposition is the answer to such problems, as explained in this paper and demonstrated on the basis of a few examples. Together with a two-level preconditioner comprising an additive Schwarz preconditioner that operates on the sub-domain level, an algebraic coarse grid preconditioner that operates on the global level, and additional load balancing measures, the described solver provides an efficient and robust solution of large systems of equations. Although the solver has been developed primarily for geomechanical problems, the ideas are applicable to the solution of other physical problems involving large differences in material properties.