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.

翻译：本文研究了激光束焊接过程的高分辨率有限元模拟。该过程的热力学行为通过一组热弹性方程建模，形成一个非线性、非对称的鞍点系统。采用牛顿法处理非线性问题，并应用适当的区域分解预处理器以加速求解所有线性化系统的迭代方法的收敛性。由于单层Schwarz预处理器通常不具备可扩展性，必须引入第二层。因此，本文提出了一种采用GDSW（广义Dryja-Smith-Widlund）粗空间及其经济变体的整体双层重叠Schwarz方法的构建与数值分析。