On some parallel algorithms for metacomputing

We discuss the design of parallel algorithms for metacomputing on distant Parallel computer or clusters linked by a slow network. As a matter of fact local network of processors are still one or two order of magnitude at least faster than long distant network used for metacomputing. Efficient parallel algorithms that rely on fast communication have been extensively developed in the past: we intend to use them for parallel computation within the clusters. On top of these local parallel algorithms, new robust and parallel algorithms are needed that can work with few clusters linked by a slow communication network. We present two algorithms of this type. First we have developed a family of adaptive time marching schemes (C(p,q,j) schemes) designed to couple system of differential equations. Second, we design a new family of two level domain decomposition algorithms that matche the multicluster architecture. These algorithms are based on the acceleration of the Schwarz domain decomposition method. We illustrate the concept of our method with solving linear and non linear problems as combustion problems on distant parallel computer.