4.3 Domain decomposition and basic numerical routines

The data distribution with respect to domain decomposition uses geometrical connections for the parallelization. The domain $\Omega$ will be split into $P$ subdomains $\Omega _i$ ( $i=\overline{1,P} \makebox[0pt]{}$), whose will be mapped on a process. Fig. 4.4 presents an part of a non-overlapping domain decomposition. We denote edges between subdomain as Interfaces. The overlapping domain decomposition is not the main scope of that chapter.

Figure 4.4: Non-overlapping domain decomposition.

Concerning the data type we distinguish between element based and node based data, which we may store overlapping or non-overlapping (Domains are still non-overlapped!). This leads to 4 types of data distributions - we will investigate the non-overlapping distribution of (finite) elements in detail. We regard matrices which have been generated by Finite Element Methods (FEM), Finite Difference Methods (FDM) or Finite Volume Methods (FVM).