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Prof. Dr. Axel Klawonn

Director

University of Cologne
Department of Mathematics and Computer Science
Division of Mathematics
Weyertal 86 - 90, 50931 Köln
Phone: +49 (0) 221 470 - 7868/7861
Email: axel.klawonn(at)uni-koeln.de
URL: numerik.uni-koeln.de
ORCID: 0000-0003-4765-7387

CDS Research Areas

CDS Selected Projects

Efficient numerical methods for the simulation of problems from computational science and engineering (CSE) are in the focus of research of Axel Klawonn and his research group. This comprises the development of efficient numerical algorithms, their theoretical analysis and implementation on large parallel computers with up to several hundreds of thousands of cores and up to more than a million MPI ranks. A special emphasis in the applications is currently given to problems in computational biology and medicine, continuum mechanics, and material science. Axel Klawonn and his co-workers have made major contributions to the field of highly parallel scalable domain decomposition methods for partial differential equations and to parallel scalable computational scale bridging/multiscale methods. He and his group have a high expertise in high performance computing (HPC) and they are involved in national and international projects on extreme scale computing. Recently, scientific machine learning (SciML) has been added to his research topics. For further details, see Research Klawonn.

Computational Fluid Dynamics (CFD) Simulation on a Benchmark Geometry with an Aritificial Aneurysm

Selected publications

  1. Tommaso Bevilacqua, Axel Klawonn, Martin Lanser, “Highly Scalable Two-level Monolithic Overlapping Schwarz Preconditioners for Thermo-elastoplastic Laser Beam Welding Problems”. Computational Mechanics, Springer, 2025. https://doi.org/10.1007/s00466-025-02674-6, Preprint.
  2. Viktor Grimm, Alexander Heinlein, Axel Klawonn, "Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks". Journal of Computational Physics, vol 535, Elsevier, 2025, https://doi.org/10.1016/j.jcp.2025.114027.
  3. Axel Klawonn, Martin Lanser, Janine Weber, "Machine learning and domain decomposition methods - a survey". Comput. Sci. Eng., Springer, 2024. https://link.springer.com/article/10.1007/s44207-024-00003-y, Preprint.​​​​​​​
  4. Axel Klawonn, Martin Lanser, Janine Weber, "A Domain Decomposition-Based CNN-DNN Architecture for Model Parallel Training Applied to Image Recognition Problems". SIAM J. Sci. Comput, Vol 46(5), 2024. https://doi.org/10.1137/23M1562202, https://arxiv.org/abs/2302.06564
  5. Axel Klawonn, Stephan Köhler, Martin Lanser, Oliver Rheinbach, "Computational Homogenization with Million-way Parallelism using Domain Decomposition Methods". Computational Mechanics, Springer Nature, 65, pp. 1-22, 2020. Published online in July 2019. Preprint, Shared Link, and https://doi.org/10.1007/s00466-019-01749-5.
  6. 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.
  7. Axel Klawonn, Martin Lanser, Oliver Rheinbach, and Matthias Uran. "Nonlinear FETI-DP and BDDC Methods: A Unified Framework and Parallel Results", SIAM J. Sci. Comput. 39 (2017), no. 6, C417–C451. doi.org/10.1137/16M1102495.
  8. Daniel Balzani, Simone Deparis, Simon Fausten, Davide Forti, Alexander Heinlein, Axel Klawonn, Alfio Quarteroni, Oliver Rheinbach, and Jörg Schröder, “Numerical Modeling of Fluid-Structure Interaction in Arteries with Anisotropic Polyconvex Hyperelastic and Anisotropic Viscoelastic Material Models at Finite Strains”, Int. J. Numer. Methods Biomed. Eng (IJNMBE), 2015. Published online December 7, 2015, http://dx.doi.org/10.1002/cnm.2756 Preprint
  9. Axel Klawonn and Olof B. Widlund, Dual-Primal FETI Methods for Linear Elasticity, Comm. Pure Appl. Math., Vol. 59, No. 11, pp.1523-1572, November 2006, http://dx.doi.org/10.1002/cpa.20156 .
  10. Axel Klawonn, Olof B. Widlund, and Maximilian Dryja, Dual-Primal FETI Methods for Three-Dimensional Elliptic Problems with Heterogeneous Coefficients , SIAM J. Numer. Anal., April 2002, Vol. 40, No. 1, pp. 159-179, http://dx.doi.org/10.1137/S0036142901388081.

For a full list of publications, see here or ORCID.