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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. For further details, see Research Klawonn.

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

Selected publications

  1. 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.
  2. Alexander Heinlein, Axel Klawonn, Oliver Rheinbach, "A Parallel Implementation of a Two-Level Overlapping Schwarz Method with an Energy-Minimizing Coarse Space based on Trilinos", SIAM J. Sci. Comp. 38 (2016), No. 6, pp. C713-C747Preprint and http://dx.doi.org/10.1137/16M1062843.
  3. 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.
  4. Axel Klawonn, Martin Lanser, Oliver Rheinbach, "FE^2TI: Computational Scale Bridging for Dual-Phase Steels". Proceedings of ParCo 2015, pp. 797 - 806, IOS Series: Advances in Parallel Computing, Volume 27, Parallel Computing: On the Road to Exascale, 2016. Preprint.
  5. 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
  6. Daniel Balzani, Dirk Böse, Dominik Brands, Raimund Erbel, Axel Klawonn, Oliver Rheinbach, Jörg Schröder, "Parallel Simulation of Patient-specific Atherosclerotic Arteries for the Enhancement of Intravascular Ultrasound Diagnistics". Engineering Computations, Vol. 29 No. 8, pp. 888-906 (2012) http://dx.doi.org/10.1137/130920563
  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 .