||Parallel elliptic PDE solver
||Grooss, Jesper (Informatics and Mathematical Modelling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
||Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
||The problem considered is how to parallelize an elliptic PDE solver, or to be specific: How to parallelize a Poisson solver based on a finite volume discretization. The Poisson problem arises as a subproblem in computational fluid dynamics (CFD). The motivation is a wish to parallelize an existing CFD solver called NS3.
Different methods from domain decomposition are presented, and their properties are outlined. First is presented the original method of Schwarz, the classical alternating Schwarz method, which is based on overlapping domains. Secondly is presented a non overlapping approach, where Dirichlet data and Neumann data are exchanged over the boundary in odd and even iterations respectively. Finally Schur Complement methods and
the BDD preconditioner are presented. In the literature the latter shows for a finite element approach nice properties from a parallelization point of view.
These methods of domain decomposition are adapted to fit into restrictions given by NS3. Numerical experiments show that the BDD preconditioner still has the same properties using a finite volume approach, hence it is applicable to the Poisson problem at hand.
Creation date: 2006-06-22
Update date: 2007-09-11