Domain decomposition methods in computational mechanics. (English) Zbl 0802.73079

Summary: The purpose is to describe domain decomposition techniques from the point of view of nonlinear mechanics. This description is complemented by a rigorous theoretical analysis which explains the key features of their success, namely: the introduction of algorithms which are consistent from the mechanical point of view and which can be written indifferently in terms of matrices or in terms of partial differential equations, the presence of a coarse global solver when solving elliptic problems on a large number of subdomains, and the ability to handle heterogeneous operators, complex geometries or unstructured partitions.


74S30 Other numerical methods in solid mechanics (MSC2010)
76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs