An optimization-based domain decomposition method for a nonlinear problem. (English) Zbl 1023.65129
Summary: A nonoverlapping domain decomposition method for the solution of a nonlinear problem is presented. The method is based on optimization to seek the Neumann boundary conditions on the interfaces between subdomains. We show that solutions of the minimization problem exist and derive an optimality system from which these solutions may be determined. We also examine finite element approximations of the solutions of the optimality system. The domain decomposition method is then reformulated as a nonlinear least-squares problem and the results of numerical experiments are given.
MSC:
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
Keywords:
nonlinear elliptic equation; nonoverlapping domain decomposition method; finite element; nonlinear least-squares problem; numerical experimentsReferences:
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