PhD Student, Group Krause
Group “High-Performance Methods for Numerical Simulation in Science, Medicine and Engineering”
I am part of the project “ExaSolvers – Extreme scale solvers for coupled problems” within the DFG Priority Programme “Software for Exascale Computing”. The aim of the project is to develop a time-parallel method for diffusion problems on heterogeneous domains arising from computational medicine. The project is conducted with international collaborators from Germany and the United States.
In particular, I am interested in parallel multilevel solvers for the solution of systems arising from space-time discretizations.
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.
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
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.
L. Grasedyck, C. L ̈obbert, G. Wittum, A. N ̈agel, V. Schulz, M. Sieben- born, R. Krause, P. Benedusi, Uwe Ku ̈ster, and Bj ̈orn 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.
X. Li, P. Benedusi, and R. Krause. An Iterative Approach for Time Integration Based on Discontinuous Galerkin Methods. arXiv preprint arXiv:1610.01324, 2016. Submitted to Mathematics of Computation.