Publications
- Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber, "Machine Learning in Adaptive Domain Decomposition Methods -Predicting the Geometric Location of Constraints". SIAM J. Sci. Comput. 41 (2019), no. 6, A3887-A3912. Preprint and https://doi.org/10.1137/18M1205364.
- Axel Klawonn, Martin Lanser, Oliver Rheinbach, Janine Weber. "Preconditioning the coarse problem of BDDC methods - Three-level, algebraic multigrid, and vertex-based preconditioners". Electronic Transaction on Numerical Analysis, 2019, Volume 51, pp. 432-450, 2019. Preprint and https://doi.org/10.1553/etna_vol51s432
- Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber, "Machine Learning in Adaptive FETI-DP - A Comparison of Smart and Random Training Data". Domain Decomposition Methods in Science and Engineering XXV. DD 2018. Lecture Notes in Computational Science and Engineering, vol 138. Springer, Cham, 2020. https://doi.org/10.1007/978-3-030-56750-7_24 and Preprint.
- Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "A Frugal FETI-DP and BDDC Coarse Space for Heterogeneous Problems". Electronic Transactions on Numerical Analysis (ETNA), Vol. 53, pp. 562-591, 2020. Preprint and https://doi.org/10.1553/etna_vol53s562.
Accepted for publication
- Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "Machine Learning in Adaptive FETI-DP - Reducing the Effort in Sampling". Submitted for publication in the proceedings of the ENUMATH 2019 conference, Springer LNCSE, Accepted April 2020. Preprint.
Submitted for publication
- Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "Combining Machine Learning and Adaptive Coarse Spaces - A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions". Submitted June 2020. Preprint.
- Viktor Grimm, Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "Estimating the time-dependent contact rate of SIR and SEIR models in mathematical epidemiology using physics-informed neural networks". Submitted September 2020. Preprint.
- Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "Combining Machine Learning and Domain Decomposition Methods - A Review". Submitted to GAMM Mitteilungen, October 2020. Preprint.