Parallel preconditioners in ParPre

The ParPre package contains preconditioners that are specifically designed for execution on parallel computers. For this, we have taken two approaches in the design of the package:

1.

Certain preconditioners are based on subdomain partitioning of the physical problem. In the context of the matrix-vector equation to be solved, this corresponds to a partitioning of the problem variables. On each subdomain, a sub-system is then solved by a classical, uni-processor preconditioner or solver. This class of preconditioners comprises Schwarz methods, Schur complement domain decomposition, and block factorisation methods. This last category can reduce to classical methods such as ILU(0) for certain parameter settings.

2.

Other preconditioners are based on multi-colourings of the problem variables. Given a multi-colouring and a simple partitioning of the problem variables, one can reasonably expect each colour to be present on each processor in roughly equal measure.

This class of preconditioners comprises multi-colour SSOR and ILU factorisations, and various types of algebraic multigrid.