On the nonlinear domain decomposition method
The known abstract framework of the subspace iteration method for linear problems is generalized to the nonlinear case. The proposed method requires the solution of local nonlinear problems and a global problem. The presented analysis shows (under relatively weak assumptions) that the nonlinear iteration converges locally at the same asymptotic rate as the corresponding linear iteration applied to the linearized problem. The analysis is similar to the technique developed in the multigrid method for nonlinear problems. Next, conditions which guarantee the global convergence of the method are discussed. It should be noted that the proposed algorithm uses different strategies depending on whether the iterates are in a neighbourhood of the solution or outside.
scientific article; zbMATH DE number 1033761