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 | 59 | 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 | 58 | 2016 |
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 | 54 | 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 | 49 | 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 | 44 | 2019 |
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 | 38 | 2019 |
FROSch: A fast and robust overlapping Schwarz domain decomposition preconditioner based on Xpetra in Trilinos A Heinlein, A Klawonn, S Rajamanickam, O Rheinbach Domain Decomposition Methods in Science and Engineering XXV 25, 176-184, 2020 | 34 | 2020 |
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 | 30 | 2022 |
Stationary flow predictions using convolutional neural networks M Eichinger, A Heinlein, A Klawonn Numerical Mathematics and Advanced Applications ENUMATH 2019: European …, 2020 | 27 | 2020 |
Parallel overlapping Schwarz preconditioners and multiscale discretizations with applications to fluid-structure interaction and highly heterogeneous problems A Heinlein Universität zu Köln, 2016 | 27 | 2016 |
The approximate component mode synthesis special finite element method in two dimensions: parallel implementation and numerical results A Heinlein, U Hetmaniuk, A Klawonn, O Rheinbach Journal of computational and applied mathematics 289, 116-133, 2015 | 26 | 2015 |
Improving the parallel performance of overlapping Schwarz methods by using a smaller energy minimizing coarse space A Heinlein, A Klawonn, O Rheinbach, OB Widlund Domain Decomposition Methods in Science and Engineering XXIV 24, 383-392, 2018 | 24* | 2018 |
An adaptive GDSW coarse space for two-level overlapping Schwarz methods in two dimensions A Heinlein, A Klawonn, J Knepper, O Rheinbach Domain Decomposition Methods in Science and Engineering XXIV 24, 373-382, 2018 | 23 | 2018 |
Surrogate convolutional neural network models for steady computational fluid dynamics simulations M Eichinger, A Heinlein, A Klawonn Universität zu Köln, 2020 | 20 | 2020 |
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 | 19 | 2020 |
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 | 18* | 2019 |
Combining Machine Learning and Adaptive Coarse Spaces---A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions A Heinlein, A Klawonn, M Lanser, J Weber SIAM Journal on Scientific Computing 43 (5), S816-S838, 2021 | 17 | 2021 |
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 | 16 | 2022 |
Additive and hybrid nonlinear two-level Schwarz methods and energy minimizing coarse spaces for unstructured grids A Heinlein, M Lanser SIAM Journal on Scientific Computing 42 (4), A2461-A2488, 2020 | 16 | 2020 |
A three-level extension of the GDSW overlapping Schwarz preconditioner in three dimensions A Heinlein, A Klawonn, O Rheinbach, F Röver Domain Decomposition Methods in Science and Engineering XXV 25, 185-192, 2020 | 16 | 2020 |