3 citations · 8 across the 21 of their papers we have counts for
19 papers · 1 filter
Two-level additive Schwarz preconditioners with GDSW coarse spaces for high-order discretizations in 2D
Tommaso Bevilacqua, Axel Klawonn, Martin Lanser +1
Two-level overlapping Schwarz preconditioners with Generalized Dryja-Smith-Widlund (GDSW) and Reduced GDSW (RGDSW) coarse spaces for high-order finite element methods (FEM) and vir…
Mixture of experts surrogate model for the homogenization of open-porous materials
Axel Klawonn, Martin Lanser, Lucas Mager +2
For open-porous materials, incorporating their microstructural properties into mechanical simulations poses a significant challenge for accurately capturing elastic deformation. To…
Learning Adaptive Coarse Spaces Using Transferable Neural Network Models for Linear and Nonlinear Overlapping Domain Decomposition Methods
Axel Klawonn, Martin Lanser, Janine Weber-Hamacher
Domain decomposition methods have been established as efficient and parallel scalable iterative solvers and preconditioners for the solution of large-scale systems arising from the…
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…
Preconditioning a Fluid--Structure Interaction Problem Using Monolithic and Block Domain Decomposition Methods for the Fluid
Axel Klawonn, Jascha Knepper, Lea Saßmannshausen
A fluid-structure interaction (FSI) problem is solved via a monolithic coupling of the fluid, structure, and geometry subproblems. The iterative GMRES solver is accelerated with th…
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…
A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulations
Simon Klaes, Axel Klawonn, Natalie Kubicki +4
This work aims to predict blood flow with non-Newtonian viscosity in stenosed arteries using convolutional neural network (CNN) surrogate models. An alternating Schwarz domain deco…
Monolithic and Block Overlapping Schwarz Preconditioners for the Incompressible Navier-Stokes Equations
Alexander Heinlein, Axel Klawonn, Jascha Knepper +1
Monolithic preconditioners applied to the linear systems arising during the solution of the discretized incompressible Navier-Stokes equations are typically more robust than precon…
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…
Adaptive and frugal BDDC coarse spaces for virtual element discretizations of a Stokes problem with heterogeneous viscosity
Tommaso Bevilacqua, Axel Klawonn, Martin Lanser
The virtual element method (VEM) is a family of numerical methods to discretize partial differential equations on general polygonal or polyhedral computational grids. However, the…
Monolithic overlapping Schwarz preconditioners for nonlinear finite element simulations of laser beam welding processes
Tommaso Bevilacqua, Axel Klawonn, Martin Lanser +1
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 e…
Computational homogenization for aerogel-like polydisperse open-porous materials using neural network--based surrogate models on the microscale
Axel Klawonn, Martin Lanser, Lucas Mager +1
The morphology of nanostructured materials exhibiting a polydisperse porous space, such as aerogels, is very open porous and fine grained. Therefore, a simulation of the deformatio…
Learning Adaptive Constraints in Nonlinear FETI-DP Methods
Axel Klawonn, Martin Lanser, Janine Weber
While linear FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) is an efficient iterative domain decomposition solver for discretized linear PDEs (partial different…
Machine learning and domain decomposition methods -- a survey
Axel Klawonn, Martin Lanser, Janine Weber
Hybrid algorithms, which combine black-box machine learning methods with experience from traditional numerical methods and domain expertise from diverse application areas, are prog…
Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks
Viktor Grimm, Alexander Heinlein, Axel Klawonn
In recent years, the concept of introducing physics to machine learning has become widely popular. Most physics-inclusive ML-techniques however are still limited to a single geomet…
A computational framework for pharmaco-mechanical interactions in arterial walls using parallel monolithic domain decomposition methods
Daniel Balzani, Alexander Heinlein, Axel Klawonn +5
A computational framework is presented to numerically simulate the effects of antihypertensive drugs, in particular calcium channel blockers, on the mechanical response of arterial…