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Preprints, Working Papers or Reports

Grimm, Viktor ORCID: 0000-0001-5300-3705, Heinlein, Alexander ORCID: 0000-0003-1578-8104 and Klawonn, Axel ORCID: 0000-0003-4765-7387 (2022). A short note on solving partial differential equations using convolutional neural networks. Technical Report.

Klawonn, Axel ORCID: 0000-0003-4765-7387 and Lanser, Martin ORCID: 0000-0002-4232-9395 (2022). Efficient Adaptive Elimination Strategies in Nonlinear FETI-DP Methods in Combination with Adaptive Spectral Coarse Spaces. Technical Report.

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Wasiak, Adam ORCID: 0000-0002-5705-9754 (2022). Three-level BDDC for Virtual Elements. Technical Report.

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Weber, Janine ORCID: 0000-0002-6692-2230 (2022). Adaptive Three-level BDDC Using Frugal Constraints. Technical Report.

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Weber, Janine ORCID: 0000-0002-6692-2230 (2022). Learning Adaptive FETI-DP Constraints for Irregular Domain Decompositions. Technical Report.

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Weber, Janine ORCID: 0000-0002-6692-2230 (2022). Learning Adaptive Coarse Basis Functions of FETI-DP. Technical Report.

Balzani, Daniel ORCID: 0000-0002-1422-4262, Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Rheinbach, Oliver ORCID: 0000-0002-9310-8533 and Schröder, Jörg (2022). Comparison of Arterial Wall Models in Fluid-Structure Interaction Simulations. Technical Report.

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Wasiak, Adam (2021). Adaptive and Frugal FETI-DP for Virtual Elements. Technical Report.

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387 and Lanser, Martin ORCID: 0000-0002-4232-9395 (2021). Adaptive Nonlinear Domain Decomposition Methods. Technical Report.

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin, Rheinbach, Oliver ORCID: 0000-0002-9310-8533 and Uran, Matthias (2021). Fully-Coupled Micro-Macro Finite Element Simulations of the Nakajima Test Using Parallel Computational Homogenization. Technical Report.

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Uran, Matthias (2021). Adaptive Nonlinear Elimination in Nonlinear FETI-DP Methods. Technical Report.

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine (2021). Predicting the geometric location of critical edges in adaptive GDSW overlapping domain decomposition methods using deep learning. Technical Report.

Eichinger, Matthias, Heinlein, Alexander ORCID: 0000-0003-1578-8104 and Klawonn, Axel ORCID: 0000-0003-4765-7387 (2020). Surrogate Convolutional Neural Network Models for Steady Computational Fluid Dynamics Simulations. Technical Report.

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine (2020). Combining Machine Learning and Domain Decomposition Methods – A Review. Technical Report.

Grimm, Viktor, Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine (2020). Estimating the time-dependent contact rate of SIR and SEIR models in mathematical epidemiology using physics-informed neural networks. Technical Report.

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Knepper, Jascha ORCID: 0000-0002-8769-2235, Rheinbach, Oliver and Widlund, Olof B. (2020). Adaptive GDSW coarse spaces of reduced dimension for overlapping Schwarz methods. Technical Report.

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine (2020). Combining Machine Learning and Adaptive Coarse Spaces - A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions. Technical Report.

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Hochmuth, Christian and Klawonn, Axel ORCID: 0000-0003-4765-7387 (2019). Fully algebraic two-level overlapping Schwarz preconditioners for elasticity problems. Technical Report.

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine (2019). Machine Learning in Adaptive FETI-DP - Reducing the Effort in Sampling. Technical Report.

Eichinger, Matthias, Heinlein, Alexander ORCID: 0000-0003-1578-8104 and Klawonn, Axel ORCID: 0000-0003-4765-7387 (2019). Stationary flow predictions using convolutional neural networks. Technical Report.

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine (2019). A Frugal FETI-DP and BDDC Coarse Space for Heterogeneous Problems. Technical Report.

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin, Rheinbach, Oliver and Weber, Janine (2019). Preconditioning the coarse problem of BDDC methods - Three-level, algebraic multigrid, and vertex-based preconditioners. Technical Report.

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Hochmuth, Christian and Klawonn, Axel ORCID: 0000-0003-4765-7387 (2019). Reduced Dimension GDSW Coarse Spaces for Monolithic Schwarz Domain Decomposition Methods for Incompressible Fluid Flow Problems. Technical Report.

Giese, Daniel, Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Knepper, Jascha ORCID: 0000-0002-8769-2235 and Peters, Kristina ORCID: 0000-0003-3064-0247 (2019). Comparison of MRI measurements and CFD simulations of hemodynamics in intracranial aneurysms using a 3D printed model - A benchmark problem. Technical Report.

Giese, Daniel, Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Knepper, Jascha ORCID: 0000-0002-8769-2235 and Peters, Kristina ORCID: 0000-0003-3064-0247 (2019). Comparison of MRI measurements and CFD simulations of hemodynamics in intracranial aneurysms using a 3D printed model - Influence of noisy MRI measurements. Technical Report.

Klawonn, Axel ORCID: 0000-0003-4765-7387, Köhler, Stephan, Lanser, Martin and Rheinbach, Oliver (2019). Computational Homogenization with Million-way Parallelism using Domain Decomposition Methods. Technical Report.

Klawonn, Axel ORCID: 0000-0003-4765-7387, Kühn, Martin Joachim ORCID: 0000-0002-0906-6984 and Rheinbach, Oliver (2019). Parallel adaptive FETI-DP using lightweight asynchronous dynamic load balancing. Technical Report.

Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Rajamanickam, Sivasankaran and Rheinbach, Oliver (2018). FROSch: A Fast And Robust Overlapping Schwarz Domain Decomposition Preconditioner Based on Xpetra in Trilinos. Technical Report.

Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387 and Kühn, Martin Joachim ORCID: 0000-0002-0906-6984 (2018). Local spectra of adaptive domain decomposition methods. Technical Report.

Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine (2018). Machine Learning in Adaptive FETI-DP - A Comparison of Smart and Random Training Data. Technical Report.

Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Rheinbach, Oliver and Röver, Friederike (2018). A Three-Level Extension of the GDSW Overlapping Schwarz Preconditioner in Three Dimensions. Technical Report.

Klawonn, Axel ORCID: 0000-0003-4765-7387, Kühn, Martin Joachim ORCID: 0000-0002-0906-6984 and Rheinbach, Oliver (2018). A closer look at local eigenvalue solvers for adaptive FETI-DP and BDDC. Technical Report.

Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Knepper, Jascha ORCID: 0000-0002-8769-2235 and Rheinbach, Oliver (2018). Adaptive GDSW coarse spaces for overlapping Schwarz methods in three dimensions. Technical Report.

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin Heinrich, Rheinbach, Oliver, Wellein, Gerhard and Wittmann, Markus (2018). Energy Efficiency of Nonlinear Domain Decomposition Methods. Technical Report.

Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin Heinrich and Weber, Janine (2018). Machine Learning in adaptive domain decomposition methods - predicting the geometric location of constraints. Technical Report.

Heinlein, Alexander, Hochmuth, Christian and Klawonn, Axel ORCID: 0000-0003-4765-7387 (2018). Monolithic Overlapping Schwarz Domain Decomposition Methods with GDSW Coarse Spaces for Saddle Point Problems. Technical Report.