Domain Decomposition and Variational Methods

There are several reasons to study Domain Decomposition Methods (DDM) • For Parallel Processing, because it is an easy way to allocate tasks to processors in a multi-processor machine. • For local mesh refinements, by putting a numerical zoom around the re-gions in which one wants a better precision. • For new applications such as thermal studies in buildings, or preliminary studies for car for instance in the art design departments where construc-tive solid geometry is prefered to engineering CAD systems. For the second item Professor J.L. Lions suggested a method where by the space of the variational formulation is decomposed. For example for the Dirichlet problem in Ω ∫