Universität zu Köln

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Wasiak, Adam ORCID: 0000-0002-5705-9754 (2023). Adaptive and Frugal FETI-DP for Virtual Elements. Vietnam J. Math., 51 (1). S. 89 - 112. SINGAPORE: SPRINGER SINGAPORE PTE LTD. ISSN 2305-2228

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.

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Knepper, Jascha ORCID: 0000-0002-8769-2235, Rheinbach, Oliver ORCID: 0000-0002-9310-8533 and Widlund, Olof B. (2022). ADAPTIVE GDSW COARSE SPACES OF REDUCED DIMENSION FOR OVERLAPPING SCHWARZ METHODS. SIAM J. Sci. Comput., 44 (3). S. A1176 - 29. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

Grimm, Viktor ORCID: 0000-0001-5300-3705, Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine ORCID: 0000-0002-6692-2230 (2022). ESTIMATING THE TIME-DEPENDENT CONTACT RATE OF SIR AND SEIR MODELS IN MATHEMATICAL EPIDEMIOLOGY USING PHYSICS-INFORMED NEURAL NETWORKS. Electron. Trans. Numer. Anal., 56. S. 1 - 28. KENT: KENT STATE UNIVERSITY. ISSN 1068-9613

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.

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine (2021). COMBINING MACHINE LEARNING AND ADAPTIVE COARSE SPACES---A HYBRID APPROACH FOR ROBUST FETI-DP METHODS IN THREE DIMENSIONS. SIAM J. Sci. Comput., 43 (5). S. S816 - 23. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

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. Comput. Mech., 68 (5). S. 1153 - 1179. NEW YORK: SPRINGER. ISSN 1432-0924

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.

Klawonn, Axel ORCID: 0000-0003-4765-7387, Koehler, Stephan, Lanser, Martin ORCID: 0000-0002-4232-9395 and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2020). Computational homogenization with million-way parallelism using domain decomposition methods. Comput. Mech., 65 (1). S. 1 - 23. NEW YORK: SPRINGER. ISSN 1432-0924

Klawonn, Axel ORCID: 0000-0003-4765-7387, Kuhn, Martin J. ORCID: 0000-0002-0906-6984 and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2020). Parallel adaptive FETI-DP using lightweight asynchronous dynamic load balancing. Int. J. Numer. Methods Eng., 121 (4). S. 621 - 644. HOBOKEN: WILEY. ISSN 1097-0207

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Hochmuth, Christian and Klawonn, Axel ORCID: 0000-0003-4765-7387 (2020). Reduced dimension GDSW coarse spaces for monolithic Schwarz domain decomposition methods for incompressible fluid flow problems. Int. J. Numer. Methods Eng., 121 (6). S. 1101 - 1120. HOBOKEN: WILEY. ISSN 1097-0207

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 ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Knepper, Jascha and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2019). ADAPTIVE GDSW COARSE SPACES FOR OVERLAPPING SCHWARZ METHODS IN THREE DIMENSIONS. SIAM J. Sci. Comput., 41 (5). S. A3045 - 28. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine (2019). MACHINE LEARNING IN ADAPTIVE DOMAIN DECOMPOSITION METHODS-PREDICTING THE GEOMETRIC LOCATION OF CONSTRAINTS. SIAM J. Sci. Comput., 41 (6). S. A3887 - 26. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Hochmuth, Christian and Klawonn, Axel ORCID: 0000-0003-4765-7387 (2019). MONOLITHIC OVERLAPPING SCHWARZ DOMAIN DECOMPOSITION METHODS WITH GDSW COARSE SPACES FOR INCOMPRESSIBLE FLUID FLOW PROBLEMS. SIAM J. Sci. Comput., 41 (4). S. C291 - 26. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

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. Electron. Trans. Numer. Anal., 51. S. 432 - 451. KENT: KENT STATE UNIVERSITY. ISSN 1068-9613

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.

Klawonn, Axel ORCID: 0000-0003-4765-7387, Kuehn, Martin and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2018). ADAPTIVE FETI-DP AND BDDC METHODS WITH A GENERALIZED TRANSFORMATION OF BASIS FOR HETEROGENEOUS PROBLEMS. Electron. Trans. Numer. Anal., 49. S. 1 - 28. KENT: KENT STATE UNIVERSITY. ISSN 1068-9613

Brenner, Susanne, Cai, Xiao-Chuan, Gander, Martin J., Klawonn, Axel ORCID: 0000-0003-4765-7387, Sarkis, Marcus and Szyld, Daniel B. (2018). Dedicated to Olof B. Widlund on the occasion of his 80th birthday. Electron. Trans. Numer. Anal., 49. S. VII - 2. KENT: KENT STATE UNIVERSITY. ISSN 1068-9613

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Knepper, Jascha and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2018). MULTISCALE COARSE SPACES FOR OVERLAPPING SCHWARZ METHODS BASED ON THE ACMS SPACE IN 2D. Electron. Trans. Numer. Anal., 48. S. 156 - 183. KENT: KENT STATE UNIVERSITY. ISSN 1068-9613

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2018). NONLINEAR BDDC METHODS WITH APPROXIMATE SOLVERS. Electron. Trans. Numer. Anal., 49. S. 244 - 274. KENT: KENT STATE UNIVERSITY. ISSN 1068-9613

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395, Rheinbach, Oliver ORCID: 0000-0002-9310-8533 and Uran, Matthias (2017). NONLINEAR FETI-DP AND BDDC METHODS: A UNIFIED FRAMEWORK AND PARALLEL RESULTS. SIAM J. Sci. Comput., 39 (6). S. C417 - 35. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

Klawonn, Axel ORCID: 0000-0003-4765-7387, Kuehn, Martin and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2016). ADAPTIVE COARSE SPACES FOR FETI-DP IN THREE DIMENSIONS. SIAM J. Sci. Comput., 38 (5). S. A2880 - 32. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

Klawonn, Axel ORCID: 0000-0003-4765-7387, Radtke, Patrick and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2016). A COMPARISON OF ADAPTIVE COARSE SPACES FOR ITERATIVE SUBSTRUCTURING IN TWO DIMENSIONS. Electron. Trans. Numer. Anal., 45. S. 75 - 107. KENT: KENT STATE UNIVERSITY. ISSN 1068-9613

Balzani, Daniel ORCID: 0000-0002-1422-4262, Deparis, Simone ORCID: 0000-0002-2832-6630, Fausten, Simon, Forti, Davide, Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Quarteroni, Alfio, Rheinbach, Oliver ORCID: 0000-0002-9310-8533 and Schroeder, Joerg (2016). Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains. Int. J. Numer. Meth. Biomed., 32 (10). HOBOKEN: WILEY. ISSN 2040-7947

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387 and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2016). A PARALLEL IMPLEMENTATION OF A TWO-LEVEL OVERLAPPING SCHWARZ METHOD WITH ENERGY-MINIMIZING COARSE SPACE BASED ON TRILINOS. SIAM J. Sci. Comput., 38 (6). S. C713 - 35. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2015). TOWARD EXTREMELY SCALABLE NONLINEAR DOMAIN DECOMPOSITION METHODS FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS. SIAM J. Sci. Comput., 37 (6). S. C667 - 30. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

Hetmaniuk, Ulrich and Klawonn, Axel ORCID: 0000-0003-4765-7387 (2014). ERROR ESTIMATES FOR A TWO-DIMENSIONAL SPECIAL FINITE ELEMENT METHOD BASED ON COMPONENT MODE SYNTHESIS. Electron. Trans. Numer. Anal., 41. S. 109 - 133. KENT: KENT STATE UNIVERSITY. ISSN 1068-9613

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Rheinbach, Oliver ORCID: 0000-0002-9310-8533 (2014). NONLINEAR FETI-DP AND BDDC METHODS. SIAM J. Sci. Comput., 36 (2). S. A737 - 29. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197