Block-Triangular Preconditioners for Saddle Point Problems with a Penalty Term. - Axel Klawonn (SIAM J. Sci. Comput., 1998)

An Optimal Preconditioner for a Class of Saddle Point Problems with a Penalty Term. - Axel Klawonn (SIAM J. Sci. Comput., 1998)

Block triangular preconditioners for nonsymmetric saddle point problems: field-of-values analysis. - Axel Klawonn; Gerhard Starke (Numerische Mathematik, 1999)

A comparison of overlapping Schwarz methods and block preconditioners for saddle point problems. - Axel Klawonn; Luca F. Pavarino (Numer. Linear Algebra Appl., 2000)

A Domain Decomposition Method with Lagrange Multipliers and Inexact Solvers for Linear Elasticity. - Axel Klawonn; Olof B. Widlund (SIAM J. Sci. Comput., 2000)

A FETI Domain Decomposition Method for Edge Element Approximations in Two Dimensions with Discontinuous Coefficients. - Andrea Toselli; Axel Klawonn (SIAM J. Numer. Anal., 2001)

Dual-Primal FETI Methods for Three-Dimensional Elliptic Problems with Heterogeneous Coefficients. - Axel Klawonn; Olof B. Widlund; Maksymilian Dryja (SIAM J. Numer. Anal., 2002)

A preconditioner for the equations of linear elasticity discretized by the PEERS element. - Axel Klawonn; Gerhard Starke (Numer. Linear Algebra Appl., 2004)

A Parallel Implementation of Dual-Primal FETI Methods for Three-Dimensional Linear Elasticity Using a Transformation of Basis. - Axel Klawonn; Oliver Rheinbach (SIAM J. Sci. Comput., 2006)

Domain Decomposition for Less Regular Subdomains: Overlapping Schwarz in Two Dimensions. - Clark R. Dohrmann; Axel Klawonn; Olof B. Widlund (SIAM J. Numer. Anal., 2008)

An Analysis of a FETI-DP Algorithm on Irregular Subdomains in the Plane. - Axel Klawonn; Oliver Rheinbach; Olof B. Widlund (SIAM J. Numer. Anal., 2008)

Projector preconditioning and transformation of basis in FETI-DP algorithms for contact problems. - Marta Jarosová; Axel Klawonn; Oliver Rheinbach (Math. Comput. Simul., 2012)

Analysis of FETI-DP and BDDC for Linear Elasticity in 3D with Almost Incompressible Components and Varying Coefficients Inside Subdomains. - Sabrina Gippert; Axel Klawonn; Oliver Rheinbach (SIAM J. Numer. Anal., 2012)

Deflation, Projector Preconditioning, and Balancing in Iterative Substructuring Methods: Connections and New Results. - Axel Klawonn; Oliver Rheinbach (SIAM J. Sci. Comput., 2012)

A Deflation Based Coarse Space in Dual-Primal FETI Methods for Almost Incompressible Elasticity. - Sabrina Gippert; Axel Klawonn; Oliver Rheinbach (ENUMATH, 2013)

A Simultaneous Augmented Lagrange Approach for the Simulation of Soft Biological Tissue. - Dirk Böse; Sarah Brinkhues; Raimund Erbel; Axel Klawonn; Oliver Rheinbach; Jörg Schröder (Domain Decomposition Methods in Science and Engineering XX, 2013)

FETI-DP for Elasticity with Almost Incompressible Material Components. - Sabrina Gippert; Axel Klawonn; Oliver Rheinbach (Domain Decomposition Methods in Science and Engineering XX, 2013)

Nonlinear FETI-DP and BDDC Methods. - Axel Klawonn; Martin Lanser; Oliver Rheinbach (SIAM J. Sci. Comput., 2014)

Parallel Two-Level Overlapping Schwarz Methods in Fluid-Structure Interaction. - Alexander Heinlein; Axel Klawonn; Oliver Rheinbach (ENUMATH, 2015)

A Highly Scalable Implementation of Inexact Nonlinear FETI-DP Without Sparse Direct Solvers. - Axel Klawonn; Martin Lanser; Oliver Rheinbach (ENUMATH, 2015)

FE2TI: Computational Scale Bridging for Dual-Phase Steels. - Axel Klawonn; Martin Lanser; Oliver Rheinbach (PARCO, 2015)

The approximate component mode synthesis special finite element method in two dimensions: Parallel implementation and numerical results. - Alexander Heinlein; Ulrich Hetmaniuk; Axel Klawonn; Oliver Rheinbach (J. Comput. Appl. Math., 2015)

FETI-DP Methods with an Adaptive Coarse Space. - Axel Klawonn; Patrick Radtke; Oliver Rheinbach (SIAM J. Numer. Anal., 2015)

Toward Extremely Scalable Nonlinear Domain Decomposition Methods for Elliptic Partial Differential Equations. - Axel Klawonn; Martin Lanser; Oliver Rheinbach (SIAM J. Sci. Comput., 2015)

A Parallel Implementation of a Two-Level Overlapping Schwarz Method with Energy-Minimizing Coarse Space Based on Trilinos. - Alexander Heinlein; Axel Klawonn; Oliver Rheinbach (SIAM J. Sci. Comput., 2016)

Adaptive Coarse Spaces for FETI-DP in Three Dimensions. - Axel Klawonn; Martin J. Kühn; Oliver Rheinbach (SIAM J. Sci. Comput., 2016)

Scalability of Classical Algebraic Multigrid for Elasticity to Half a Million Parallel Tasks. - Allison H. Baker; Axel Klawonn; Tzanio V. Kolev; Martin Lanser; Oliver Rheinbach; Ulrike Meier Yang (Software for Exascale Computing, 2016)

One-Way and Fully-Coupled FE2 Methods for Heterogeneous Elasticity and Plasticity Problems: Parallel Scalability and an Application to Thermo-Elastoplasticity of Dual-Phase Steels. - Daniel Balzani; Ashutosh Gandhi; Axel Klawonn; Martin Lanser; Oliver Rheinbach; Jörg Schröder (Software for Exascale Computing, 2016)

Nonlinear FETI-DP and BDDC Methods: A Unified Framework and Parallel Results. - Axel Klawonn; Martin Lanser; Oliver Rheinbach; Matthias Uran (SIAM J. Sci. Comput., 2017)

Multicore Performance Engineering of Sparse Triangular Solves Using a Modified Roofline Model. - Markus Wittmann; Georg Hager; Radim Janalík; Martin Lanser; Axel Klawonn; Oliver Rheinbach; Olaf Schenk; Gerhard Wellein (SBAC-PAD, 2018)

Stationary Flow Predictions Using Convolutional Neural Networks. - Matthias Eichinger; Alexander Heinlein; Axel Klawonn (ENUMATH, 2019)

Fully Algebraic Two-Level Overlapping Schwarz Preconditioners for Elasticity Problems. - Alexander Heinlein; Christian Hochmuth; Axel Klawonn (ENUMATH, 2019)

Machine Learning in Adaptive FETI-DP: Reducing the Effort in Sampling. - Alexander Heinlein; Axel Klawonn; Martin Lanser; Janine Weber (ENUMATH, 2019)

Monolithic Overlapping Schwarz Domain Decomposition Methods with GDSW Coarse Spaces for Incompressible Fluid Flow Problems. - Alexander Heinlein; Christian Hochmuth; Axel Klawonn (SIAM J. Sci. Comput., 2019)

Adaptive GDSW Coarse Spaces for Overlapping Schwarz Methods in Three Dimensions. - Alexander Heinlein; Axel Klawonn; Jascha Knepper; Oliver Rheinbach (SIAM J. Sci. Comput., 2019)

Machine Learning in Adaptive Domain Decomposition Methods - Predicting the Geometric Location of Constraints. - Alexander Heinlein; Axel Klawonn; Martin Lanser; Janine Weber (SIAM J. Sci. Comput., 2019)

EXASTEEL: Towards a Virtual Laboratory for the Multiscale Simulation of Dual-Phase Steel Using High-Performance Computing. - Axel Klawonn; Martin Lanser; Matthias Uran; Oliver Rheinbach; Stephan Köhler; Jörg Schröder; Lisa Scheunemann; Dominik Brands; Daniel Balzani; Ashutosh Gandhi; Gerhard Wellein; Markus Wittmann; et al. (Software for Exascale Computing, 2020)

Energy efficiency of nonlinear domain decomposition methods. - Axel Klawonn; Martin Lanser; Oliver Rheinbach; Gerhard Wellein; Markus Wittmann (Int. J. High Perform. Comput. Appl., 2021)

Combining Machine Learning and Adaptive Coarse Spaces - A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions. - Alexander Heinlein; Axel Klawonn; Martin Lanser; Janine Weber (SIAM J. Sci. Comput., 2021)

Adaptive GDSW Coarse Spaces of Reduced Dimension for Overlapping Schwarz Methods. - Alexander Heinlein; Axel Klawonn; Jascha Knepper; Oliver Rheinbach; Olof B. Widlund (SIAM J. Sci. Comput., 2022)

A computational framework for pharmaco-mechanical interactions in arterial walls using parallel monolithic domain decomposition methods. - Daniel Balzani; Alexander Heinlein; Axel Klawonn; Jascha Knepper; Sharan Nurani Ramesh; Oliver Rheinbach; Lea Sassmannshausen; Klemens Uhlmann (CoRR, 2023)

Machine learning and domain decomposition methods - a survey. - Axel Klawonn; Martin Lanser; Janine Weber (CoRR, 2023)

Learning Adaptive Constraints in Nonlinear FETI-DP Methods. - Axel Klawonn; Martin Lanser; Janine Weber (CoRR, 2023)

Adaptive Nonlinear Domain Decomposition Methods with an Application to the $p$-Laplacian. - Alexander Heinlein; Axel Klawonn; Martin Lanser (SIAM J. Sci. Comput., 2023)

Computational homogenization for aerogel-like polydisperse open-porous materials using neural network-based surrogate models on the microscale. - Axel Klawonn; Martin Lanser; Lucas Mager; Ameya Rege (CoRR, 2024)

Monolithic overlapping Schwarz preconditioners for nonlinear finite element simulations of laser beam welding processes. - Tommaso Bevilacqua; Axel Klawonn; Martin Lanser; Adam Wasiak (CoRR, 2024)

Model Parallel Training and Transfer Learning for Convolutional Neural Networks by Domain Decomposition. - Axel Klawonn; Martin Lanser; Janine Weber (CoRR, 2024)

Adaptive and frugal BDDC coarse spaces for virtual element discretizations of a Stokes problem with heterogeneous viscosity. - Tommaso Bevilacqua; Axel Klawonn; Martin Lanser (CoRR, 2024)

Nonlinear Monolithic Two-Level Schwarz Methods for the Navier-Stokes Equations. - Axel Klawonn; Martin Lanser (CoRR, 2024)

Domain-decomposed image classification algorithms using linear discriminant analysis and convolutional neural networks. - Axel Klawonn; Martin Lanser; Janine Weber (CoRR, 2024)

Nonlinear Two-Level Schwarz Methods: A Parallel Implementation in FROSch. - Alexander Heinlein; Kyrill Ho; Axel Klawonn; Martin Lanser (CoRR, 2024)

A Domain Decomposition-Based CNN-DNN Architecture for Model Parallel Training Applied to Image Recognition Problems. - Axel Klawonn; Martin Lanser; Janine Weber (SIAM J. Sci. Comput., 2024)

Learning adaptive coarse basis functions of FETI-DP. - Axel Klawonn; Martin Lanser; Janine Weber (J. Comput. Phys., 2024)

A continuous benchmarking infrastructure for high-performance computing applications. - Christoph Alt; Martin Lanser; Jonas Plewinski; Atin Janki; Axel Klawonn; Harald Köstler; Michael Selzer; Ulrich Rüde (Int. J. Parallel Emergent Distributed Syst., 2024)

Towards Automated Algebraic Multigrid Preconditioner Design Using Genetic Programming for Large-Scale Laser Beam Welding Simulations. - Dinesh Parthasarathy; Tommaso Bevilacqua; Martin Lanser; Axel Klawonn; Harald Köstler (PASC, 2025)

Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks. - Viktor Grimm; Alexander Heinlein; Axel Klawonn (J. Comput. Phys., 2025)

Highly Scalable Two-level Monolithic Overlapping Schwarz Preconditioners for Thermo-elastoplastic Laser Beam Welding Problems. - Tommaso Bevilacqua; Axel Klawonn; Martin Lanser (CoRR, 2025)

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; Philipp Hartwig; Axel Klawonn; Martin Lanser; Michael Rethmeier; Lisa Scheunemann; Jörg Schröder (CoRR, 2025)

Monolithic and Block Overlapping Schwarz Preconditioners for the Incompressible Navier-Stokes Equations. - Alexander Heinlein; Axel Klawonn; Jascha Knepper; Lea Sassmannshausen (CoRR, 2025)