Universität zu Köln

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.

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

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). 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, Perego, Mauro and Rajamanickam, Sivasankaran (2021). FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica. 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

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 (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.

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.

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Rheinbach, Oliver, Röver, Friederike, Sandfeld, Stefan and Steinberger, Dominik (2019). Applying the FROSch Overlapping Schwarz Preconditioner for Dislocation Mechanics in Deal.II. 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.

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 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

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

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