On the Accuracy of the Inner Newton Iteration in Nonlinear Domain Decomposition
We introduce an energy minimizing nonlinear preconditioner for our nonlinear FETI-DP methods, and we will show numerical results for some problems in two dimensions based on the scaled p-Laplace operator. The equivalence of nonlinear FETI-DP methods and specific right-preconditioned Newton-Krylov methods was already shown. In nonlinear FETI-DP methods, the preconditioner describes a nonlinear elimination process. In the variants proposed here, the evolution of a problem dependent global energy is controlled during the elimination process, which guarantees that the application of the nonlinear preconditioner does not increase the global energy. Often, stopping the inner Newton iteration early, based on the energy criterion, gives better performance of the overall method. In this paper, a comparison of the classical nonlinear FETI-DP methods with nonlinear FETI-DP methods using an energy minimizing nonlinear preconditioner is provided.
This work was supported in part by the German Research Foundation (DFG) through the Priority Programme 1648 “Software for Exascale Computing” (SPPEXA) under grants KL 2094/4-1, KL 2094/4-2, RH 122/2-1, and RH 122/3-2.
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