Universität zu Köln

2023

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

2022

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 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 Coarse Basis Functions of FETI-DP. 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.

2021

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.

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

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.

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, 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

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

2020

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

Heinlein, Alexander and Lanser, Martin ORCID: 0000-0002-4232-9395 (2020). ADDITIVE AND HYBRID NONLINEAR TWO-LEVEL SCHWARZ METHODS AND ENERGY MINIMIZING COARSE SPACES FOR UNSTRUCTURED GRIDS. SIAM J. Sci. Comput., 42 (4). S. A2461 - 28. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

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

2019

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.

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, 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.

Heinlein, Alexander ORCID: 0000-0003-1578-8104 and Lanser, Martin (2019). Additive and Hybrid Nonlinear Two-Level Schwarz Methods and Energy Minimizing Coarse Spaces for Unstructured Grids. 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, 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

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.

2018

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 and Lanser, Martin (2018). Coarse Spaces for Nonlinear Schwarz Methods on Unstructured Grids. Technical Report.

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

2017

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

2015

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

2014

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