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Center for Data and Simulation Science

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.

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

Selected publications

  1. 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.
  2. 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.
  3. Alexander Heinlein, Christian Hochmuth, Axel Klawonn, "Monolithic Overlapping Schwarz Domain Decomposition Methods with GDSW Coarse Spaces for Incompressible Fluid Flow Problems". SIAM J. Sci. Comput. 41 (2019), no. 4, C291–C316. Preprint and https://doi.org/10.1137/18M1184047. PDF version.
  4. 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. pdf version.
  5. Allison H. Baker, Axel Klawonn, Tzanio Kolev, Martin Lanser, Oliver Rheinbach, Ulrike Meier Yang, "Scalability of Classical Algebraic Multigrid for Elasticity to Half a Million Parallel Tasks", Software for Exascale Computing - SPPEXA 2013-2015, vol. 113 Springer LNCSE, pages 113--140, 2016, Preprint.
  6. 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.2756Preprint
  7. Dominik Brands, Axel Klawonn, Oliver Rheinbach, and Jörg Schröder, Modeling and convergence in arterial wall simulations using a parallel FETI solution strategy, Computer Methods in Biomechanics and Biomedical Engineering, Vol. 11, No. 5, October 2008, pp. 569-583, http://dx.doi.org/10.1080/10255840801949801 .

  8. Axel Klawonn and Oliver Rheinbach , Inexact FETI-DP Methods , Inter. J. Numer. Methods Engrg., Vol. 69, pp. 284-307, January 2007, published electronically June 2006, http://dx.doi.org/10.1002/nme.1758 .

  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 .