| Multilevel domain decomposition-based architectures for physics-informed neural networks V Dolean, A Heinlein, S Mishra, B Moseley Computer Methods in Applied Mechanics and Engineering 429, 117116, 2024 | 105 | 2024 |
| Combining machine learning and domain decomposition methods for the solution of partial differential equations—A review A Heinlein, A Klawonn, M Lanser, J Weber GAMM‐Mitteilungen 44 (1), e202100001, 2021 | 98 | 2021 |
| Numerical modeling of fluid–structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains D Balzani, S Deparis, S Fausten, D Forti, A Heinlein, A Klawonn, ... International journal for numerical methods in biomedical engineering 32 (10 …, 2016 | 66 | 2016 |
| Adaptive GDSW coarse spaces for overlapping Schwarz methods in three dimensions A Heinlein, A Klawonn, J Knepper, O Rheinbach SIAM Journal on Scientific Computing 41 (5), A3045-A3072, 2019 | 64 | 2019 |
| Multiscale coarse spaces for overlapping Schwarz methods based on the ACMS space in 2D A Heinlein, A Klawonn, J Knepper, O Rheinbach Verlag der Österreichischen Akademie der Wissenschaften, 2018 | 61 | 2018 |
| A parallel implementation of a two-level overlapping Schwarz method with energy-minimizing coarse space based on Trilinos A Heinlein, A Klawonn, O Rheinbach SIAM Journal on Scientific Computing 38 (6), C713-C747, 2016 | 61 | 2016 |
| Finite basis kolmogorov-arnold networks: domain decomposition for data-driven and physics-informed problems AA Howard, B Jacob, S Helfert, A Heinlein, P Stinis arXiv preprint arXiv:2406.19662, 2024 | 51 | 2024 |
| Estimating the time-dependent contact rate of SIR and SEIR models in mathematical epidemiology using physics-informed neural networks V Grimm, A Heinlein, A Klawonn, M Lanser, J Weber Electron. Trans. Numer. Anal 56, 1-27, 2022 | 50 | 2022 |
| FROSch: A fast and robust overlapping Schwarz domain decomposition preconditioner based on Xpetra in Trilinos A Heinlein, A Klawonn, S Rajamanickam, O Rheinbach International Conference on Domain Decomposition Methods, 176-184, 2018 | 49 | 2018 |
| Machine Learning in Adaptive Domain Decomposition Methods---Predicting the Geometric Location of Constraints A Heinlein, A Klawonn, M Lanser, J Weber SIAM Journal on Scientific Computing 41 (6), A3887-A3912, 2019 | 47 | 2019 |
| Surrogate convolutional neural network models for steady computational fluid dynamics simulations M Eichinger, A Heinlein, A Klawonn Universität zu Köln, 2020 | 33 | 2020 |
| Finite basis physics-informed neural networks as a Schwarz domain decomposition method V Dolean, A Heinlein, S Mishra, B Moseley International Conference on Domain Decomposition Methods, 165-172, 2022 | 31 | 2022 |
| The approximate component mode synthesis special finite element method in two dimensions A Heinlein, U Hetmaniuk, A Klawonn, O Rheinbach Journal of computational and applied mathematics 289 (C), 116-133, 2015 | 30 | 2015 |
| Monolithic overlapping Schwarz domain decomposition methods with GDSW coarse spaces for incompressible fluid flow problems A Heinlein, C Hochmuth, A Klawonn SIAM Journal on Scientific Computing 41 (4), C291-C316, 2019 | 29* | 2019 |
| Parallel overlapping Schwarz preconditioners and multiscale discretizations with applications to fluid-structure interaction and highly heterogeneous problems A Heinlein Universität zu Köln, 2016 | 29 | 2016 |
| Stationary flow predictions using convolutional neural networks M Eichinger, A Heinlein, A Klawonn Numerical Mathematics and Advanced Applications ENUMATH 2019: European …, 2020 | 28 | 2020 |
| Improving the parallel performance of overlapping Schwarz methods by using a smaller energy minimizing coarse space A Heinlein, A Klawonn, O Rheinbach, OB Widlund International Conference on Domain Decomposition Methods, 383-392, 2017 | 28* | 2017 |
| Reduced dimension GDSW coarse spaces for monolithic Schwarz domain decomposition methods for incompressible fluid flow problems A Heinlein, C Hochmuth, A Klawonn International Journal for Numerical Methods in Engineering 121 (6), 1101-1119, 2020 | 27 | 2020 |
| An adaptive GDSW coarse space for two-level overlapping Schwarz methods in two dimensions A Heinlein, A Klawonn, J Knepper, O Rheinbach International Conference on Domain Decomposition Methods, 373-382, 2017 | 25 | 2017 |
| Adaptive GDSW coarse spaces of reduced dimension for overlapping Schwarz methods A Heinlein, A Klawonn, J Knepper, O Rheinbach, OB Widlund SIAM Journal on Scientific Computing 44 (3), A1176-A1204, 2022 | 23 | 2022 |
Axel KlawonnProfessor of Applied Mathematics, Universität zu Köln/University of CologneVerified email at uni-koeln.de
