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Two-level nonlinear Schwarz methods - a parallel implementation with application to nonlinear elasticity and incompressible flow problems
Kyrill Ho, Axel Klawonn, Martin Lanser
Nonlinear Schwarz methods are a type of nonlinear domain decomposition method used as an alternative to Newton's method for solving discretized nonlinear partial differential equat…
Towards a parallel Schwarz solver framework for virtual elements using GDSW coarse spaces
Tommaso Bevilacqua, Axel Klawonn, Martin Lanser +1
The Virtual Element Method (VEM) is used to perform the discretization of the Poisson problem on polygonal and polyhedral meshes. This results in a symmetric positive definite line…
Large-scale Thermo-Mechanical Simulation of Laser Beam Welding Using High-Performance Computing: A Qualitative Reproduction of Experimental Results
Tommaso Bevilacqua, Andrey Gumenyuk, Niloufar Habibi +6
Laser beam welding is a non-contact joining technique that has gained significant importance in the course of the increasing degree of automation in industrial manufacturing. This…
Highly Scalable Two-level Monolithic Overlapping Schwarz Preconditioners for Thermo-elastoplastic Laser Beam Welding Problems
Tommaso Bevilacqua, Axel Klawonn, Martin Lanser
A thermo-elastoplastic finite element approach is used to perform the simulation of a laser beam welding (LBW) process. This results in a nonlinear, nonsymmetric saddle point multi…
Nonlinear Two-Level Schwarz Methods: A Parallel Implementation in FROSch
Alexander Heinlein, Kyrill Ho, Axel Klawonn +1
Owing to the ability of nonlinear domain decomposition methods to improve the nonlinear convergence behavior of Newton's method, they have experienced a rise in popularity recently…
Nonlinear Monolithic Two-Level Schwarz Methods for the Navier-Stokes Equations
Axel Klawonn, Martin Lanser
Nonlinear domain decomposition methods became popular in recent years since they can improve the nonlinear convergence behavior of Newton's method significantly for many complex pr…