Solution of elliptic partial differential equations by an optimization-based domain decomposition method

摘要

An optimization-based, non-overlapping domain decomposition method for the solution of elliptic partial differential equations is presented. The crux of the method is a constrained minimization problem for which the objective functional measures the jump in the dependent variables across the common boundaries between subdomains; the constraints are the partial differential equations. The method is reformulated as a linear least-squares problem. The latter is examined and a conjugate gradient method for its solution is presented and analyzed. The results of some numerical experiments are also given.