5. Vectorization and parallelization of iterative methods

In this chapter, we solve systems of linear equations like

$$K_{n\times n} \cdot \underline{x}\;=\;\underline{b} \enspace,$$ (5.1)

using iterative methods. The system of equations above was generated by discretization of a differential operator. Matrix $K$ is sparse if FEM (Finite Element Method), FDM (Finite Differences Method) or FVM (Finite Volume Method) have been used for discretization. In the following, we assume exactly this sparsity pattern of the matrix.

All parallel algorithms refer to section 4.3 and especially to non-overlapping element distribution 4.3.1. The appropriate vector and matrix types are denoted in the same way as therein.
The use of any other data distribution in the parallelization will be emphasized explicitly.