2 citations · 5 across the 18 of their papers we have counts for
20 papers
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…
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…
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…
Towards Automated Algebraic Multigrid Preconditioner Design Using Genetic Programming for Large-Scale Laser Beam Welding Simulations
Dinesh Parthasarathy, Tommaso Bevilacqua, Martin Lanser +2
Multigrid methods are asymptotically optimal algorithms ideal for large-scale simulations. But, they require making numerous algorithmic choices that significantly influence their…
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…
Domain-decomposed image classification algorithms using linear discriminant analysis and convolutional neural networks
Axel Klawonn, Martin Lanser, Janine Weber
In many modern computer application problems, the classification of image data plays an important role. Among many different supervised machine learning models, convolutional neura…
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…
Model Parallel Training and Transfer Learning for Convolutional Neural Networks by Domain Decomposition
Axel Klawonn, Martin Lanser, Janine Weber
Deep convolutional neural networks (CNNs) have been shown to be very successful in a wide range of image processing applications. However, due to their increasing number of model p…
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…
A Continuous Benchmarking Infrastructure for High-Performance Computing Applications
Christoph Alt, Martin Lanser, Jonas Plewinski +5
For scientific software, especially those used for large-scale simulations, achieving good performance and efficiently using the available hardware resources is essential. It is im…
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…
A Domain Decomposition-Based CNN-DNN Architecture for Model Parallel Training Applied to Image Recognition Problems
Axel Klawonn, Martin Lanser, Janine Weber
Deep neural networks (DNNs) and, in particular, convolutional neural networks (CNNs) have brought significant advances in a wide range of modern computer application problems. Howe…