5.4.4 Parallel algorithms

The update step of the Gauß-Seidel iteration is the significant difference to the Jacobi iteration so we restrict our further investigations on it. A data distribution with non-overlapping elements (Sec. 4.3.1) is assumed and represented in Fig. 5.4.

Figure 5.4: Domain decomposition of unit square

A formal application of the parallelization strategy used for the $\omega$-Jacobi iteration results in a distributed matrix  ${\ensuremath{\color{green}{\sf K}}}$, an accumulated diagonal matrix  ${\ensuremath{\color{red}\mathfrak{D}}}$, distributed stored vectors $\underline{{\ensuremath{\color{green}{\sf f}}}}$, $\underline{{\ensuremath{\color{green}{\sf r}}}}$ and accumulated vectors $\underline{{\ensuremath{\color{red}\mathfrak{u}}}}^k$, $\underline{{\ensuremath{\color{red}\mathfrak{w}}}}$. In difference to the Jacobi iteration we have to investigate various opportunities for choosing an efficient parallel algorithm.