This research unit brings together a selected core team of researchers from Aachen, Bochum,
Cologne, Düsseldorf, and Stuttgart, and one associated PI from Munich. This selection combines
expertise in numerical methods and mathematical modeling as well as junior and established levels.
All PIs have extensive experience
in interdisciplinary collaborations between applied mathematicians and computational physicists or
Spokesperson of the research unit: Manuel Torrilhon (RWTH Aachen)
Co-Spokesperson of the research unit: Christiane Helzel (Heinrich-Heine-University Düsseldorf)
In alphabetical order, the PIs and their qualifications are given below, including the associated PI.
Stefanie Braun’s expertise lies in the mathematical description of fluid and kinetic systems in the presence of electromagnetic fields. She has considerable experience in the field of plasma physics, where she has worked on different aspects of particle transport in hot fusion plasmas Braun, Helander (2010), Braun, Helander et al. (2009), Fülöp, Braun, Pusztai (2010) and on spin effects in quantum plasmas Braun, Asenjo, Mahajan (2012). More recently, Dr. Braun has focused on the modeling of electrochemical systems for battery applications, where she developed a mathematical model for ionic transport in a solid electrolyte Braun, Yada, Latz (2015) that has gained increasing attention in the community. One emphasis lies on the thermodynamic consistency of the model, ensuring the mathematical well-behavedness of the system by rigorously demanding an entropy principle in the derivation of the constitutive laws. In contrast to earlier models, this system can be derived based on first principles only. Dr. Braun is currently a postdoctoral fellow at the Center for Computational Engineering Sciences at RWTH Aachen, where she works, together with the FZ Jülich, on the development of a numerical multi-scale hybrid scheme combining thermodynamics and ab-initio methods to simulate dendritic growth in solid electrolytes.
Personal website with contact information: ACoM
Jürgen Dreher is a senior scientist in the theoretical physics institute at the Ruhr-University Bochum. He has a background in space plasma theory where he investigated the Hall effect in magnetic reconnection using numerical simulations Dreher, Schindler (1997) and devised a dynamical model of magnetosphere-ionosphere coupling Dreher (1997), among other topics. He was the key developer of the distributed-parallel adaptive mesh refinement framework racoon Dreher, Grauer (2005), which has been the basis for numerous scientific projects in plasma physics and fluid dynamics Dreher, Laveder et al. (2005), Grafke, Homann, Dreher, Grauer (2008). Dr. Dreher oversaw the theoretical modeling and related numerical studies of the “FlareLab” plasma experiment, operated in Bochum Tacke, Dreher, Sydora (2013). More recently, he developed interest in the field of cardiac electrophysiology, which is actually closely related to plasma physics as both address the collective dynamics of charged particles under the influence of self-consistent fields, and hence can be described by similar macroscopic model equations. Here, Dr. Dreher gives lectures on Computational Cardiology as part of the Medical Physics curriculum in Bochum, and he has supervised theses on parametric shape optimization in the monodomain model and on Purkinje-Myocardium coupling.
Personal website with contact information: TP1
Gregor Gassner and his group work on the development, analysis and efficient implementation of structure-preserving schemes, for nonlinear conservation laws, such as, e.g., the compressible Navier-Stokes or the visco-resistive magnetohydrodynamics equations Bohm, Winters, Gassner et al. (2020), Derigs, Winters, Gassner, Walch (2016), Gassner, Winters et al. (2018), Gassner, Winters, Kopriva (2016). He combines concepts from summation-by-parts finite difference methods with standard nodal DG strategies to develop new schemes, such as split-form DG methods, e.g., in Wintermeyer, Winters, Gassner, Warburton (2018), that allow to preserve auxiliary quantities such as, e.g., entropy or kinetic energy. These novel developments have successfully impacted the high-order DG community, as shown by the invited plenary talk at ICOSAHOM 2018 and the invitation to write a review paper for ‘Frontiers in Physics’ special issue ’Rising Stars’. Dr. Gassner is co-author of several simulation codes, with the newest iteration being Trixi.jl, an open-source 3D AMR split-form DG solver. Since 2018 he is full professor for Applied Mathematics and Scientific Computing at the University of Cologne. In the context of provably stable high-order discretizations for extreme scale parallel computing, he received an ERC starting grant in 2016.
Personal website with contact information: NumSim
Rainer Grauer and his group focus on two main research directions: the non-perturbative or instanton approach to turbulence, see the review Grafke, Schäfer, Grauer (2015), and the multi-physics treatment of collisionless plasmas Rieke, Trost, Grauer (2015), Lautenbach, Grauer(2018). In the instanton approach, probability density functions of various observables could be calculated by combining theoretical methods from quantum field theory and numerical techniques from optimal control. These studies developed from earlier research on singularity formation in the incompressible Euler equations, especially analyzing the interplay between curvature and divergence of vortex lines Grafke, Grauer (2013). The multi-physics treatment of collisionless plasmas aims at performing large scale simulations of space plasma scenarios including and combining various plasma models. This approach is based on earlier work on Maxwell-Darwin Vlasov simulations Schmitz, Grauer (2006b), Schmitz, Grauer (2006c) including the back-substitution method for the semi-Lagrangian Vlasov scheme. Two fluid (5- and 10-moment) codes coupled to Maxwell's equation including a Landau-damping closure were developed in Allmann-Rahn, Trost, Grauer (2018), Allmann-Rahn, Lautenbach, Grauer (2022), Allmann-Rahn, Grauer, Kormann (2022). Dr. Grauer is heading the chair for Computational Plasma Physics and has been speaker of the DFG research unit 1048 "Instabilities, Turbulence and Transport in Cosmic Magnetic Fields" .
Personal website with contact information: TP1
Christiane Helzel’s work is devoted to the development of numerical methods for partial differential equations, with emphasis on hyperbolic and transport dominant problems. She made several contributions to the wave propagation algorithm, for example extending the method to approximate PDEs on the sphere Calhoun, Helzel, LeVeque (2008) and proposing a third order accurate version. Furthermore, she developed Cartesian grid cut cell methods for the approximation of hyperbolic problems in complex geometries Helzel, Berger, Leveque (2005). As member of the DFG-SFB611, she worked on a model for suspensions of rod-like particles Helzel, Otto (2006). This model was later extended Helzel, Tzavaras (2016, Helzel, Tzavaras (2017) to model a sedimentation process. As a member of the DFG research unit 1048, she collaborated with Dr. Dreher and Dr. Grauer and developed a constrained transport method for the three-dimensional MHD equations Helzel, Rossmanith, Taetz (2013) as well as a more accurate WENO method for Cartesian grids with adaptive mesh refinement. Recently, Dr. Helzel contributed to the development of the Active Flux method, a new multidimensional, third order accurate finite volume method Helzel, Kerkmann, Scandurra (2019. Since 2014, Dr. Helzel holds the Chair for Applied Mathematics at the Heinrich-Heine-University of Düsseldorf.
Personal website with contact information: HHU
Michael Schlottke-Lakemper focuses in his research on scalable methods for bulk- and interface-coupled multi-physics simulations, e.g., Schlottke-Lakemper, Winters et al. (2021), with an emphasis on adaptive numerical schemes for complex, large-scale problems that require high-performance computing. In Schlottke-Lakemper, Yu et al. (2017), Schlottke-Lakemper, Niemöller et al. (2019), he presented an efficient strategy for coupling heterogeneous models through a single, shared hierarchical Cartesian mesh. This approach allows to choose the spatial discretization method and grid resolution for each model independently and supports different temporal discretizations. To retain parallel efficiency, he developed a dynamic load balancing scheme to optimize the domain decomposition for coupled simulations on heterogeneous hardware Niemöller, Schlottke-Lakemper et al. (2020). By employing hybrid parallelization techniques, his simulation codes have been demonstrated to scale efficiently to more than 100,000 cores Schlottke-Lakemper, Yu et al. (2017). Furthermore, he is a principal developer of the Julia-based open-source simulation code Trixi.jl Schlottke-Lakemper, Gassner et al. (2021), Ranocha, Schlottke-Lakemper et al. (2022), and has experience with numerical methods for execution on GPU-accelerated systems Kraus, Schlottke et al. (2014). Since 2021, Dr. Schlottke-Lakemper is heading the Training and Scalable Algorithms group at the High-Performance Computing Center Stuttgart (HLRS) of the University of Stuttgart.
Personal website with contact information: HLRS
Eric Sonnendrücker is the director of the group for numerical methods for plasma physics at the Max-Planck-Institute for Plasma Physics combined with a professorship at TU Munich. He is an internationally renowned expert in mathematical modeling of plasmas and in the design and analysis of numerical methods. His specialities range from kinetic to continuum models, and both particle Kraus, Kormann, Morrison, Sonnendrücker (2017) and grid-based Crouseilles, Mehrenberger, Sonnendrücker (2010) computational approaches, including electrodynamics Pinto, Sonnendrücker (2016) and structure preservation Kormann, Sonnendrücker (2021), Crouseilles, Ratnani, Sonnendrücker (2012). Dr. Sonnendrücker is principal investigator on several EUROfusion projects and serves as associated editor for SIAM Journal on Scientific Computing and Journal of Computational Physics. He is also member of the advisory board of the Max Planck Computing and Data Facility.
Personal website with contact information: IPP
Manuel Torrilhon and his group work on numerical and mathematical analysis for plasma and gas processes, in particular hyperbolic conservation laws and moment approximation for the Boltzmann equation. His development of regularized moment equations is widely known in the community as was recently highlighted by the invited paper Torrilhon (2016) in the Annual Review of Fluid Mechanics. He also has important contributions to limiter functions of finite volume methods, e.g. Cada, Torrilhon (2009), and the construction of divergence constraint-preserving schemes for magnetohydrodynamics, e.g. Torrilhon (2005). Recently, Dr. Torrilhon developed a hierarchical simulation approach Torrilhon, Sarna (2017) that is able to scale through linear moment models and can be used to estimate model errors from model residuals. The maximum-entropy closure is the most promising technique to extend this framework to the nonlinear regime, but comes with severe computational challenges as demonstrated in Sadr, Torrilhon, Gorji, Schaerer, Bansal, Torrilhon (2017). Dr. Torrilhon’s research has been funded through several individual DFG grants. Currently, he is also member of two DFG Research Training Groups and of the National High Performance Computing Center for Computational Engineering Sciences (NHR4CES) - a joint initiative of RWTH Aachen and the TU Darmstadt.
Personal website with contact information: ACoM