Alexander Heinlein

TU Delft

DIAM, Faculty of EEMCS

Numerical Analysis

Mekelweg 4, 2628 CD Delft

Room HB 03.290

Tel.: +31 (0)15 27 89135

Alexander Heinlein is assistant professor in the Numerical Analysis group of the Delft Institute of Applied Mathematics (DIAM), Faculty of Electrical Engineering, Mathematics & Computer Science (EEMCS), at the Delft University of Technology (TU Delft).

His main research areas are numerical methods for partial differential equations and scientific computing, in particular, solvers and discretizations based on domain decomposition and multiscale approaches. He is interested in high-performance computing (HPC) and solving challenging problems involving, e.g., complex geometries, highly heterogenous coefficient functions, or the coupling of multiple physics. More recently, Alexander also started focusing on the combination of scientific computing and machine learning, a new research area also known as scientific machine learning (SciML). Generally, his work includes the development of new methods and their theoretical foundation as well as their implementation on current computer architectures (CPUs, GPUs) and application to real world problems.

news

Oct 5, 2022 New open master projects on Improving Nonlinear Solver Convergence Using Machine Learning (co-supervised by Tycho van Noorden (COMSOL)) and Domain Decomposition for Machine Learning Based Medical Imaging (co-supervised by Eric Cyr (Sandia National Laboratories)) available; see master thesis projects.
Jun 12, 2022 I am co-organizing two mini-symposia at the 7th International Domain Decomposition Conference (DD27) in Prague, July 25-29, 2022: MS4: Spectral Coarse Spaces in Domain Decomposition Methods and Multiscale Discretizations together with Vitorita Dolean Maini (University of Strathclyde and Cote d’Azur University) and Kathrin Semtana (Stevens Institute of Technology) and MS9: Learning Algorithms, Domain Decomposition Methods, and Applications together with Xiao-Chuan Cai (University of Macau) and Axel Klawonn (University of Cologne).
Jun 9, 2022 I will give an invited plenary lecture on Robust, algebraic, and scalable Schwarz preconditioners with extension-based coarse spaces at the 7th International Domain Decomposition Conference (DD27) in Prague, July 25-29, 2022.

recent publications (full list)

  1. A short note on solving partial differential equations using convolutional neural networks
    Grimm, Viktor, Heinlein, Alexander, and Klawonn, Axel
    Submitted November 2022
  2. Finite basis physics-informed neural networks as a Schwarz domain decomposition method
    Submitted November 2022
  3. Reduced order fluid modeling with generative adversarial networks
    Kemna, Mirko, Heinlein, Alexander, and Vuik, Cornelis
    Submitted October 2022
  4. First steps towards modeling the interaction of cardiovascular agents and smooth muscle activation in arterial walls
    Ramesh, Sharan Nurani, Uhlmann, Klemens, Saßmannshausen, Lea, Rheinbach, Oliver, Klawonn, Axel, Heinlein, Alexander, and Balzani, Daniel
    Submitted October 2022
  5. An Experimental Study of Two-level Schwarz Domain-Decomposition Preconditioners on GPUs
    Yamazaki, Ichitaro, Heinlein, Alexander, and Rajamanickam, Sivasankaran
    Submitted October 2022