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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.
  5. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "Machine Learning in Adaptive FETI-DP - Reducing the Effort in Sampling". Proceedings of the ENUMATH 2019 conference, Springer LNCSE, Vol. 139, pp. 593-603, 2021. Preprint.
  6. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "Combining Machine Learning and Domain Decomposition Methods for the Solution of Partial Differential Equations - A Review". In GAMM Mitteilungen, 2021. Preprint and https://onlinelibrary.wiley.com/doi/full/10.1002/gamm.202100001
  7. 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". SIAM J. Sci. Comput., 43(5):S816-S838, 2021, Special Section Copper Mountain 2020.  Preprint and https://doi.org/10.1137/20M1344913.
  8. 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". Electronic Transactions on Numerical Analysis (ETNA), Volume 56, pp. 1–27, 2022. http://doi.org/10.1553/etna_vol56s1 and Preprint.
  9. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber, "Predicting the geometric location of critical edges in adaptive GDSW overlapping domain decomposition methods using deep learning". Domain Decomposition Methods in Science and Engineering XXVI. Lecture Notes in Computational Science and Engineering, vol 145. Springer, 2023. https://link.springer.com/chapter/10.1007/978-3-030-95025-5_32, Preprint.
  10. Axel Klawonn, Martin Lanser, Janine Weber, "Learning Adaptive Coarse Basis Functions of FETI-DP". Journal of Computational Physics, Vol 496, 2023. https://doi.org/10.1016/j.jcp.2023.112587, Preprint.
  11. Axel Klawonn, Martin Lanser, Janine Weber, "Learning Adaptive FETI-DP Constraints for Irregular Domain Decompositions". Domain Decomposition Methods in Science and Engineering XXVII. Lecture Notes in Computational Science and Engineering, vol 149. Springer, 2024. https://link.springer.com/chapter/10.1007/978-3-031-50769-4_33​​​​​​​, Preprint.
  12. Axel Klawonn, Martin Lanser, Janine Weber, "Adaptive Three-level BDDC Using Frugal Constraints". Domain Decomposition Methods in Science and Engineering XXVII. Lecture Notes in Computational Science and Engineering, vol 149. Springer, 2024.​​​​​​​ https://link.springer.com/chapter/10.1007/978-3-031-50769-4_34​​​​​​​, Preprint.

Accepted for publication

  1. Axel Klawonn, Martin Lanser, Janine Weber, "A Domain Decomposition-Based CNN-DNN Architecture for Model Parallel Training Applied to Image Recognition Problems". Accepted for Publication in SIAM J. Sci. Comput, 2024. https://arxiv.org/abs/2302.06564 

Submitted for publication

  1. Axel Klawonn, Martin Lanser, Janine Weber, "Machine learning and domain decomposition methods - a survey". Submitted for Publication, 2023. Preprint.​​​​​​​
  2. Axel Klawonn, Martin Lanser, Janine Weber, "Learning Adaptive Constraints in Nonlinear FETI-DP Methods". Submitted for Publication, 2023. Preprint

 

Dissertation 

  • J. Weber. Efficient and robust FETI-DP and BDDC methods -- Approximate coarse spaces and deep learning-based adaptive coarse spaces, Doctoral Dissertation, Universität zu Köln, 2022, Online Publication.