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

TL;DR

This paper develops a monolithic two-level overlapping Schwarz preconditioner with GDSW coarse space to efficiently solve nonlinear finite element models of laser beam welding, improving convergence in large-scale simulations.

Contribution

It introduces a novel monolithic, two-level Schwarz preconditioner with GDSW coarse space tailored for nonlinear thermoelasticity problems in laser welding.

Findings

Enhanced convergence of iterative solvers for nonlinear systems.

Effective scalability demonstrated through numerical analysis.

Applicability to complex thermomechanical simulations.

Abstract

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.