Overview

Parallel computing is a key issue for various categories of numerical problems. In practice, a numerical simulation may require a very fine mesh (i.e., one containing a large number of elements) and/or may be costly in terms of CPU time (when the computation is done in a serial way). Parallel computing ^[1] is an efficient solution for large size problems (i.e., with a large number of unknowns) that are impossible to carry out using classical facilities due to size requirements and/or CPU cost. In fact, parallelism consists of spreading (distributing) the computational effort and/or the memory requirements over the different computers available.

The notion of a parallel computing process can be conceived at various levels but, here, we will mainly focus on two of these levels. Obviously, the computational stage is concerned with parallelism. In such cases, a preliminary stage consists of partitioning the domain by means of sub-domains prior to dispatching these to different processors (each of them taking charge of one sub-domain). On the other hand, it could be of interest to see what degree of parallelism could be required at the mesh generation step itself.

At the solution step, a domain decomposition method requires a partition of the domain into several sub-domains. In these, the mesh that must be constructed must have certain properties. The solution method makes use of communication processes from one sub-domain to the others. At the meshing step, a parallel computational process consists of partitioning the domain into different sub-meshes in...