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Mathematisch-Naturwissenschaftliche FakultätProf. Dr. Axel Klawonn

Journal publications

  1. Alexander Heinlein, Ulrich Hetmaniuk, Axel Klawonn, and Oliver Rheinbach, "The Approximate Component Mode Synthesis Special Finite Element Method in Two Dimensions: Parallel Implementation and Numerical Results", Journal of Computational and Applied Mathematics, Vol. 289, pp. 116-133, May 2015. http://dx.doi.org/10.1016/j.cam.2015.02.053.
  2. 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. Preprint and http://dx.doi.org/10.1002/cnm.2756.
  3. Alexander Heinlein, Axel Klawonn, and Oliver Rheinbach, "A Parallel Implementation of a Two-Level Overlapping Schwarz Method with Energy-Minimizing Coarse Space based on Trilinos", SIAM J. Sci. Comp., Vol. 38, No. 6, 2016, pp. C713-C747. Preprint and http://dx.doi.org/10.1137/16M1062843.
  4. Alexander Heinlein, Axel Klawonn, Jascha Knepper, and Oliver Rheinbach. "Multiscale Coarse Spaces for Overlapping Schwarz Methods Based on the ACMS Space in 2D", Electronic Transactions on Numerical Analysis (ETNA), Vol. 48, pp. 156-182, 2018. Preprint and https://doi.org/10.1553/etna_vol48s156.
  5. 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.
  6. Alexander Heinlein, Axel Klawonn, Jascha Knepper, Oliver Rheinbach, "Adaptive GDSW Coarse Spaces for overlapping Schwarz methods in three dimensions". SIAM J. Sci. Comput. 41 (2019), no. 5, A3045–A3072. Preprint and https://doi.org/10.1137/18M1220613.
  7. 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.
  8. Alexander Heinlein, Christian Hochmuth, Axel Klawonn. "Reduced dimension GDSW coarse spaces for monolithic Schwarz domain decomposition methods for incompressible fluid flow problems". Int. J. Numer. Methods Eng. 2020; 121: 1101– 1119. Preprint and https://doi.org/10.1002/nme.6258.
  9. Alexander Heinlein, Martin Lanser. "Additive and Hybrid Nonlinear Two-Level Schwarz Methods and Energy Minimizing Coarse Spaces for Unstructured Grids". SIAM J. Sci. Comput. 42 (2020), no. 4, A2461–A2488. Preprint and https://doi.org/10.1137/19M1276972.

Conference proceedings

  1. Daniel Balzani, Simone Deparis, Simon Fausten, Davide Forti, Alexander Heinlein, Axel Klawonn, Alfio Quarteroni, Oliver Rheinbach, and Jörg Schröder. “Aspects of Arterial Wall Simulations: Nonlinear Anisotropic Material Models and Fluid Structure Interaction”, Proceedings of the WCCM XI, 2014. Download at publisher. Preprint.
  2. Simone Deparis, Davide Forti, Alexander Heinlein, Axel Klawonn, Alfio Quarteroni, and Oliver Rheinbach. “A Comparison of Preconditioners for the Steklov-Poincare Formulation of the Fluid-Structure Coupling in Hemodynamics”. Proc. Appl. Math. Mech., 15, pp. 93-94, October 2015. http://dx.doi.org/10.1002/pamm.201510037.
  3. Alexander Heinlein, Axel Klawonn, and Oliver Rheinbach, "Parallel Two-Level Overlapping Schwarz Methods in Fluid-Structure Interaction", Proceedings of the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Ankara, September, 2015. Springer Lecture Notes on Computational Science and Engineering, Vol. 112, 2016, pp. 521-530. Preprint.
  4. Alexander Heinlein, Axel Klawonn, and Oliver Rheinbach, "Parallel Overlapping Schwarz with an Energy-Minimizing Coarse Space", Proceedings of the International Conference on Domain Decomposition Methods 23. Springer Lecture Notes on Computational Science and Engineering, Vol. 116, March 2017, pp. 353-360. Preprint and http://dx.doi.org/10.1007/978-3-319-52389-7_36.
  5. Daniel Balzani, Simon Fausten, Alexander Heinlein, Axel Klawonn, Oliver Rheinbach, and Jörg Schröder. “Steps Towards More Realistic FSI Simulations of Coronary Arteries”. Proc. Appl. Math. Mech., 17, Issue 1, pp. 187-188, December 2017. http://dx.doi.org./10.1002/pamm.201710063.
  6. Simon Fausten, Daniel Balzani, Alexander Heinlein, Axel Klawonn, Oliver Rheinbach, and Jörg Schröder. “Remarks on Fluid‐Structure Interaction Simulations in Realistic Arterial Geometries with regard to the Transmural Stress Distribution”. Proc. Appl. Math. Mech., 18, e201800312, December 2018. https://doi.org/10.1002/pamm.201800312.
  7. Alexander Heinlein, Axel Klawonn, Oliver Rheinbach, and Olof Widlund, "Improving the Parallel Performance of Overlapping Schwarz Methods by Using a Smaller Energy Minimizing Coarse Space", Proceedings of the International Conference on Domain Decomposition Methods 24. Springer Lecture Notes on Computational Science and Engineering, Vol. 125, January 2019, pp. 383-392. https://doi.org/10.1007/978-3-319-93873-8_36
  8. Alexander Heinlein, Axel Klawonn, Jascha Knepper, and Oliver Rheinbach. "An Adaptive GDSW Coarse Space for Two-Level Overlapping Schwarz Methods in Two Dimensions", Proceedings of the International Conference on Domain Decomposition Methods 24. Springer Lecture Notes on Computational Science and Engineering, Vol. 125, January 2019, pp. 373-382. https://doi.org/10.1007/978-3-319-93873-8_35
  9. Alexander Heinlein, Axel Klawonn, Oliver Rheinbach, and Friederike Röver. "A Three-Level Extension of the GDSW Overlapping Schwarz Preconditioner in Two Dimensions". Advanced Finite Element Methods with Applications: Selected Papers from the 30th Chemnitz Finite Element Symposium 2017, pp. 187-204, June 2019. Preprint and https://doi.org/10.1007/978-3-030-14244-5_10.
  10. Daniel Giese, Alexander Heinlein, Axel Klawonn, Jascha Knepper, Kristina Sonnabend, "Comparison of MRI measurements and CFD simulations of hemodynamics in intracranial aneurysms using a 3D printed model - A benchmark problem". Proc. Appl. Math. Mech., 19, e201900398, 2019. Preprint and https://doi.org/10.1002/pamm.201900398.
  11. Daniel Giese, Alexander Heinlein, Axel Klawonn, Jascha Knepper, Kristina Sonnabend, "Comparison of MRI measurements and CFD simulations of hemodynamics in intracranial aneurysms using a 3D printed model - Influence of noisy MRI measurements". Proc. Appl. Math. Mech., 19, e201900401, 2019. Preprint and https://doi.org/10.1002/pamm.201900401.
  12. Alexander Heinlein, Oliver Rheinbach, Friederike Röver, Stefan Sandfeld, Dominik Steinberger, "Applying the FROSch Overlapping Schwarz Preconditioner to Dislocation Mechanics in Deal.II". Proc. Appl. Math. Mech., 19, e201900337, 2019. Preprint and https://doi.org/10.1002/pamm.201900337.

Accepted for publication

  1. Alexander Heinlein, Axel Klawonn, Oliver Rheinbach, Friederike Röver, "A Three-Level Extension of the GDSW Overlapping Schwarz Preconditioner in Three Dimensions". Submitted for publication to the proceedings of the International Conference on Domain Decomposition Methods 25, Springer LNCSE, Accepted March 2019. Preprint.
  2. Alexander Heinlein, Axel Klawonn, Sivasankaran Rajamanickam, Oliver Rheinbach, "FROSch: A Fast And Robust Overlapping Schwarz Domain Decomposition Preconditioner Based on Xpetra in Trilinos". Submitted for publication to the proceedings of the International Conference on Domain Decomposition Methods 25, Springer LNCSE, Accepted April 2019. Preprint.
  3. Alexander Heinlein, Axel Klawonn, Martin Kühn, "Local spectra of adaptive domain decomposition methods". Submitted for publication to the proceedings of the International Conference on Domain Decomposition Methods 25, Springer LNCSE, Accepted April 2019. Preprint.
  4. Alexander Heinlein, Martin Lanser, "Coarse Spaces for Nonlinear Schwarz Methods on Unstructured Grids". Submitted for publication to the proceedings of the International Conference on Domain Decomposition Methods 25, Springer LNCSE, Accepted May 2019. Preprint.
  5. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber, "Machine Learning in Adaptive FETI-DP - A Comparison of Smart and Random Training Data". Submitted for publication to the proceedings of the International Conference on Domain Decomposition Methods 25, Springer LNCSE, Accepted May 2019. Preprint.
  6. 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 2020. Preprint.
  7. Matthias Eichinger, Alexander Heinlein, Axel Klawonn. "Stationary flow predictions using convolutional neural networks". Submitted for publication in the proceedings of the ENUMATH 2019 conference, Springer LNCSE, Accepted 2020. Preprint.
  8. Alexander Heinlein, Christian Hochmuth, Axel Klawonn. "Fully algebraic two-level overlapping Schwarz preconditioners for elasticity problems". Submitted for publication in the proceedings of the ENUMATH 2019 conference, Springer LNCSE, Accepted 2020. Preprint.

Submitted for publication

  1. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "A Frugal FETI-DP and BDDC Coarse Space for Heterogeneous Problems". Submitted November 2019. Preprint.
  2. 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.
  3. Alexander Heinlein, Axel Klawonn, Jascha Knepper, Oliver Rheinbach, Olof B. Widlund. "Adaptive GDSW coarse spaces of reduced dimension for overlapping Schwarz methods". Submitted September 2020. Preprint.

Dissertation

  • Alexander Heinlein. "Parallel Overlapping Schwarz Preconditioners and Multiscale Discretizations with Applications to Fluid-Structure Interaction and Highly Heterogeneous Problems", Dissertation, Universität zu Köln, June 2016. Download.

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