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Faculty of Mathematics and Natural SciencesProf. Dr. Axel Klawonn

Publications

  1. 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.
  2. 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
  3. 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.
  4. 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

  1. 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

  1. 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.
  2. 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​​​​​​​.
  3. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "Combining Machine Learning and Domain Decomposition Methods - A Review". Submitted to GAMM Mitteilungen, October 2020. Preprint.