6. Domain decomposition methods

We have already seen that discretization of partial differential equations leads to the resolution of high-dimensional algebraic systems; the algorithms presented above are, in general and for most applications, the most efficient on traditional computers. Today, we are witnessing an evolution in machine architecture, and over the last twenty years or so, multiprocessors have appeared on the market, machines equipped with several processors designed to work in parallel on the same application. Naturally, algorithms for the numerical resolution of partial differential equations need to be adapted to this type of supercomputer. There are several possible solutions. Either we adapt the above algorithms by running all the independent phases of the program in parallel, in order to take maximum advantage of the machine's architecture; this aspect is more a matter of computer science techniques,...