Group “High-Performance Methods for Numerical Simulation in Science, Medicine and Engineering”
I have worked on novel approaches to speed up simulations in computational medicine, fluid dynamics and astrophysics. In particular, studying and developing parallel space-time solution strategies to solve non-linear PDEs.
The solution of a time-periodic flow in a rectangular channel with an external perturbation (in red). This solution is computed with a space-time multigrid solver fully in parallel (details here).
Left: solution of a diffusion problem on a complex geometry using 4D space-time multigrid. Right: solution of a non-linear reaction-diffusion problem arising from computational electrophysiology using 4D space-time multigrid.
P. Benedusi, M. Minion and R. Krause. An Experimental Comparison of a Space-time Multigrid Methods with PFASST for a Reaction-diffusion Problem. Submitted. 2020. link
S. B. Bader, P. Benedusi, A. Quaglino, P. Zulian, and R. Krause. Space-time Multilevel Monte Carlo Methods and Their Application to Cardiac Electrophysiology. Submitted. 2019. link
P. Benedusi., P. Ferrari, C. Garoni, R. Krause, and S. Serra-Capizzano. Fast Parallel Solver for the Space-time IGA-DG Discretization of the Anisotropic Diffusion Equation. Submitted. 2019. link
P. Benedusi, X. Garoni, C. Li, R. Krause and S. Serra-Capizzano. Discontinuous Galerkin Discretization of the Heat Equation in Any Dimension: the Spectral Symbol. SIAM Journal on Matrix Analysis and Applications, 2018. link
P. Benedusi, D. Hupp, P. Arbenz, and R. Krause. A Parallel Multigrid Solver for Time–periodic Incompressible Navier–Stokes Equations in 3D. In Numerical Mathematics and Advanced Applications ENUMATH 2015, pages 265–273. Springer, 2016. link
L. Grasedyck, C. Löbbert, G. Wittum, A. Nägel, V. Schulz, M. Sieben- born, R. Krause, P. Benedusi, Uwe Küster, and Björn Dick. Space and Time Parallel Multigrid for Optimization and Uncertainty Quantification in PDE Simulations. In Software for Exascale Computing-SPPEXA 2013-2015, pages 507–523. Springer, 2016.
A. Kreienbuehl, P. Benedusi, D. Ruprecht, and R. Krause. Time-parallel Gravitational Collapse Simulation. Communications in Applied Mathematics and Computational Science, 12(1):109–128, 2017. link
X. Li, P. Benedusi, and R. Krause. An Iterative Approach for Time Integration Based on Discontinuous Galerkin Methods. 2016. link