Babamehdi, M.FZJ*

2023

Abstract: Nonlinear partial differential equations frequently arise in different fields ofscience. Discretization of the nonlinear problems usually leads to large non-linear systems. Solution of such big discretized nonlinear problems needsfast, highly scalable, and parallelize solvers.Nonlinear multigrid is a well-known method for efficiently solving nonlin-ear boundary value problems. The full approximation scheme (FAS) solvesnonlinear problems on fine and coarse grids. To smooth the nonlinear prob-lem a suitable nonlinear solver is needed and since a matrix-free implemen-tation is desirable, this form of implementation of the smoother should beplausible. For this purpose, the nonlinear additive Schwarz method (NASM)seems to be an appropriate choice. NASM converges with the same rateas linear iterations applied to the linearised equation. In addition, it is inher-ently parallel and proper to be implemented in matrix-free form.We combine FAS and NASM to obtain hybrid NASM/FAS. The FAS solvesthe nonlinear problem and the NASM is the smoother of the nonlinearboundary value problem in local subdomains on each level of the multigridmethod. Within the NASM, Jacobian-Free Newton Krylov method is usedas a solver on each subdomain. We consider different nonlinear equationsin 3D space as test problems. We investigated several parameters of themethods to have a better understanding of influence of the parameters onthe efficiency of the method and its convergence rate.

1. 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511) (POF4-511)