Monolithic overlapping Schwarz preconditioners for nonlinear finite element simulations of laser beam welding processes

Adam Wasiak; Axel Klawonn; Martin Lanser; Tommaso Bevilacqua

Monolithic overlapping Schwarz preconditioners for nonlinear finite element simulations of laser beam welding processes

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arxiv 2407.03230 v1 pith:H73ELJ45 submitted 2024-07-03 math.NA cs.NA

Tommaso Bevilacqua , Axel Klawonn , Martin Lanser , Adam Wasiak This is my paper · ORCID

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keywords schwarzbeamelementfinitelasermethodmonolithicnonlinear

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Highly resolved finite element simulations of a laser beam welding process are considered. The thermomechanical behavior of this process is modeled with a set of thermoelasticity equations resulting in a nonlinear, nonsymmetric saddle point system. Newton's method is used to solve the nonlinearity and suitable domain decomposition preconditioners are applied to accelerate the convergence of the iterative method used to solve all linearized systems. Since a onelevel Schwarz preconditioner is in general not scalable, a second level has to be added. Therefore, the construction and numerical analysis of a monolithic, twolevel overlapping Schwarz approach with the GDSW (Generalized Dryja-Smith-Widlund) coarse space and an economic variant thereof are presented here.

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Genetic programming designs flexible algebraic multigrid cycles that speed up large-scale laser beam welding simulations by up to 60% over default BoomerAMG and 25% over a hand-tuned configuration.

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