ABSTRACT
The first three sections contain a description of direct methods based on the Schur complement and domain decomposition. After the first section the coefficient matrix will be assumed to be symmetric positive definite (SPD). In Section 8.3 an MPI code will be studied that illustrates domain decomposition. Iterative methods based on P-regular splittings and domain decompositions will be described in the last three sections. Here convergence analysis will be given via the minimization of the equivalent quadratic functional. An MPI version of SOR using domain decomposition will be presented in Section 8.5. This chapter is more analysis-oriented and less application-driven.
