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Alexander Heinlein works on various challanges in numerical simulations of continuum mechanical problems. In particular, his focus lies on the development of new finite element discretizations and parallel solvers as well as their efficient and parallel implementation. He works on Fluid-Structure Interaction (FSI) and Computational Fluid Dynamics (CFD) simulations for bio-medical applications; in these simulations, special care has to be taken with respect to the models, discreizations, and solvers in order to obtain accurate and realistic results in reasonable time. Similar statements hold for simulations of highly heterogeneous multiscale problems (e.g., multiphase steels and composite materials), which are another field of Alexander Heinlein's research interests. Also, he is a core developer of the FROSch (Fast and Robust Overlapping Schwarz) solver that is used for the efficient solution of the linear problems arising in the simulations. FROSch, which is part of the Trilinos library, is a framework for parallel overlapping domain decomposition solvers that is robust, scales to tens of thousands of cores, and can be easily constructed by the user. Because it is based on the Xpetra linear algebra framework, it also suitable for be used on novel architectures, such as GPUs (Graphics Processing Units), or in efficient Uncertainty Quantification (UQ) simulations.

Benchmark for Fluid-Structure Interaction Simulations in Coronary Arteries

Selected 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.
  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. Submitted May 2015, revised version October 2015, accepted for publication October 2015. Published online December 7, 2015, Preprint.
  3. Alexander Heinlein, Axel Klawonn, and 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., Vol. 38, No. 6, December 6, 2016, pp. C713-C747. Preprint and
  4. 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", Accepted for publication to the proceedings of the International Conference on Domain Decomposition Methods 24, Springer LNCSE, February 2018.
  5. 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. Submitted August 2016. Preprint and
  6. 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
  7. 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
  8. 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.
  9. 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.
  10. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber, "Machine Learning in adaptive domain decomposition methods - predicting the geometric location of constraints". Submitted for publication to SIAM J. Sci. Comp., August 2018. Preprint.