A study on decomposition methods (Q756976)

An innovative decomposition method for the approximate solution of problems is introduced based upon successive projection approximations derived by the first author [Parallel algorithms for the finite element method. Ph. D. Thesis, Columbia Univ. (1988)]. The new method provides substantially greater freedom for decomposing a given problem into a collection of subproblems than conventional methods. An approximation can be reached by recursively searching in the collection of subproblems along a chosen search path. When applied to partial differential equations, the partitioning can be made in either the physical domain (domain decomposition) of a partial differential equation or in the associated linear space (space decomposition). The decompositions can be used to solve large-scale problems, to develop parallel algorithms and novel iterative techniques.