Research Interests

Research Interests

$\bullet$ Numerical methods for partial differential equations
$\bullet$ Scoientific Computing
$\bullet$ High-Performance Computing
$\bullet$ Design and development of numerical software
$\bullet$ Cut-cell methods
$\bullet$ Numerical methods for surface PDEs and geometric PDEs
$\bullet$ Biomedical Applications

Current Publications

Current Publications

$\bullet $ Takfarinas Medani, Juan Garcia-Prieto, Francois Tadel, Marios Antonakakis, Tim Erdbrügger, Malte Höltershinken, Wayne Mead, Sophie Schrader, Anand Joshi, Christian Engwer, Carsten H. Wolters, John C. Mosher, and Richard M. Leahy. Brainstorm-DUNEuro: An integrated and user-friendly finite element method for modeling electromagnetic brain activity. NeuroImage, 267:119851, February 2023. doi:10.1016/j.neuroimage.2022.119851.

$\bullet $ Florian Streitbürger, Gunnar Birke, Christian Engwer, and Sandra May. Dod stabilization for higher-order advection in two dimensions. arXiv e-prints, January 2023. arXiv:2301.02799.

$\bullet $ Gunnar Birke, Christian Engwer, Sandra May, and Florian Streitbürger. Dod stabilization of linear hyperbolic PDEs on general cut-cell meshes. arXiv e-prints, January 2023.

$\bullet $ Tim Erdbrügger, Andreas Westhoff, Malte Hoeltershinken, Jan-Ole Radecke, Yvonne Buschermoehle, Alena Buyx, Fabrice Wallois, Sampsa Pursiainen, Joachim Gross, Rebekka Lencer, Christian Engwer, and Carsten Wolters. Cutfem forward modeling for EEG source analysis. arXiv e-prints, November 2022. arXiv:2211.17093.

$\bullet $ Nils-Arne Dreier and Christian Engwer. A hardware-aware and stable orthogonalization framework. arXiv e-prints, April 2022. arXiv:2204.13393.

$\bullet $ Christian Engwer, Iuliu Sorin Pop, and Thomas Wick. Dynamic and weighted stabilizations of the $L$-scheme applied to a phase-field model for fracture propagation. In Numerical Mathematics and Advanced Applications ENUMATH 2019, Lecture Notes in Computational Science and Engineering, 1177–1184. August 2021. doi:10.1007/978-3-030-55874-1_117.

$\bullet $ Nils-Arne Dreier and Christian Engwer. Strategies for the vectorized Block Conjugate Gradients method. In Numerical Mathematics and Advanced Applications ENUMATH 2019, Lecture Notes in Computational Science and Engineering, 381–388. August 2021. doi:10.1007/978-3-030-55874-1_37.

$\bullet $ Christian Engwer and Sebastian Westerheide. An unfitted dG scheme for coupled bulk-surface PDEs on complex geometries. Comp. Appl. Math., 21(3):569–591, July 2021. doi:10.1515/cmam-2020-0056.

$\bullet $ Sophie Schrader, Andreas Westhoff, Maria Carla Piastra, Tuuli Miinalainen, Sampsa Pursiainen, Johannes Vorwerk, Heinrich Brinck, Carsten H. Wolters, and Christian Engwer. DUNEuro-A software toolbox for forward modeling in bioelectromagnetism. PLoS ONE, 16(6):e0252431, June 2021. doi:10.1371/journal.pone.0252431.

$\bullet $ Takfarinas Medani, Juan Garcia-Prieto, Francois Tadel, Sophie Schrader, Marios Antonakakis, Anand Joshi, Christian Engwer, Carsten H. Wolters, John C. Mosher, and Richard M. Leahy. Realistic head modeling of electromagnetic brain activity: an integrated Brainstorm-DUNEuro pipeline from MRI data to the FEM solutions. In Hilde Bosmans, Wei Zhao, and Lifeng Yu, editors, Medical Imaging 2021: Physics of Medical Imaging, volume 11595, 1321 – 1328. International Society for Optics and Photonics, February 2021. doi:10.1117/12.2580935.

$\bullet $ Alexander Grebhahn, Christian Kaltenecker, Christian Engwer, Norbert Siegmund, and Sven Apel. Lightweight, semi-automatic variability extraction: A case study on scientific computing. Empirical Software Engineering, 26(2):23, February 2021. doi:10.1007/s10664-020-09922-8.

$\bullet $ Florian Streitbürger, Christian Engwer, Sandra May, and Andreas Nüßing. Monotonicity considerations for stabilized DG cut cell schemes for the unsteady advection equation. In Fred J. Vermolen and Cornelis Vuik, editors, Numerical Mathematics and Advanced Applications ENUMATH 2019, 929–937. Springer International Publishing, January 2021. doi:10.1007/978-3-030-55874-1_92.

$\bullet $ Nils-Arne Dreier and Christian Engwer. Strategies for the Vectorized Block Conjugate Gradients method. In Fred J. Vermolen and Cornelis Vuik, editors, Numerical Mathematics and Advanced Applications ENUMATH 2019, 381–388. Springer International Publishing, January 2021.

$\bullet $ Christian Engwer and Michael Wenske. Estimating the extent of glioblastoma invasion. J. Math. Biol., 82(1):10, January 2021. doi:10.1007/s00285-021-01563-9.

$\bullet $ Gregor Corbin, Axel Klar, Christina Surulescu, Christian Engwer, Michael Wenske, Juanjo Nieto, and Juan Soler. Modeling glioma invasion with anisotropy-and hypoxia-triggered motility enhancement: From subcellular dynamics to macroscopic PDEs with multiple taxis. Mathematical Models and Methods in Applied Sciences, January 2021. doi:10.1142/S0218202521500056.

$\bullet $ Peter Bastian, Markus Blatt, Andreas Dedner, Nils-Arne Dreier, Christian Engwer, René Fritze, Carsten Gräser, Christoph Grüninger, Dominic Kempf, Robert Klöfkorn, Mario Ohlberger, and Oliver Sander. The DUNE framework: Basic concepts and recent developments. Computers and Mathematics with Applications, 81:75–112, January 2021. doi:10.1016/j.camwa.2020.06.007.

$\bullet $ Mirco Altenbernd, Nils-Arne Dreier, Christian Engwer, and Dominik Göddeke. Towards local-failure local-recovery in PDE frameworks: The case of linear solvers. In Tomáš Kozubek, Peter Arbenz, Jiří Jaroš, Lubomír Říha, Jakub Šístek, and Petr Tichý, editors, High Performance Computing in Science and Engineering, Lecture Notes in Computer Science, 17–38. Springer International Publishing, January 2021. doi:10.1007/978-3-030-67077-1_2.

$\bullet $ Natalie Emken and Christian Engwer. A reaction–diffusion–advection model for the establishment and maintenance of transport-mediated polarity and symmetry breaking. Frontiers in Applied Mathematics and Statistics, November 2020. doi:10.3389/fams.2020.570036.

$\bullet $ Peter Bastian, Mirco Altenbernd, Nils-Arne Dreier, Christian Engwer, Jorrit Fahlke, René Fritze, Markus Geveler, Dominik Göddeke, Oleg Iliev, Olaf Ippisch, Jan Mohring, Steffen Müthing, Mario Ohlberger, Dirk Ribbrock, Nikolay Shegunov, and Stefan Turek. Exa-dune—flexible PDE solvers, numerical methods and applications. In Hans-Joachim Bungartz, Severin Reiz, Benjamin Uekermann, Philipp Neumann, and Wolfgang E. Nagel, editors, Software for Exascale Computing - SPPEXA 2016-2019, pages 225–269. Cham, July 2020. doi:10.1007/978-3-030-47956-5_9.

$\bullet $ Christian Engwer, Sandra May, Andreas Nüßing, and Florian Streitbürger. A stabilized DG cut cell method for discretizing the linear transport equation. SIAM J. Sci. Comp., 42(6):A3677–A3703, January 2020. doi:10.1137/19M1268318.

$\bullet $ Christian Engwer, Iuliu Sorin Pop, and Thomas Wick. Dynamic and weighted stabilizations of the $L$-scheme applied to a phase-field model for fracture propagation. arXiv e-prints, December 2019. arXiv:1912.07096.

$\bullet $ Mario Ohlberger, Andreas Buhr, Dennis Eikhorn, Christian Engwer, and Stephan Rave. Advances in model order reduction for large scale or multi-scale problems. Oberwolfach Reports, 2019:38–40, September 2019.

$\bullet $ Christian Engwer, Patrick Henning, Axel Målqvist, and Daniel Peterseim. Efficient implementation of the localized orthogonal decomposition method. Comput. Methods Appl. Mech. Engrg., 350:123–153, June 2019. doi:10.1016/j.cma.2019.02.040.

$\bullet $ Tuuli Miinalainen, Atena Rezaei, Defne Us, Andreas Nüßing, Christian Engwer, Carsten H. Wolters, and Sampsa Pursiainen. A realistic, accurate and fast source modeling approach for the EEG forward problem. NeuroImage, 184:56 – 67, January 2019. doi:10.1016/j.neuroimage.2018.08.054.