SC²S Colloquium - Aug 8, 2018
|Date:||Aug 08, 2018|
|Time:||15:00 - 16:00|
Markus Müller: Parallel Solving and Preconditioning of Bidiagonal Matrices
This is a Bachelor's Thesis submission talk advised by Thomas Huckle
The solving of linear systems in parallel is important for high performance computing. Parallelizable iterative techniques exist but are partly not suitable to handle ill-conditioned systems effectively. Preconditioners such as incomplete LU-factorization (ILU) can improve the condition of the linear system but are inherently sequential themselves. In this thesis, the incomplete sparse approximate inverse preconditioner (ISAI), a preconditioner designed for parallel environments, is applied on the case of bidiagonal matrices. Numerical characteristics are discussed and an efficient implementation presented.
Keywords: incomplete LU-factorization (ILU), incomplete sparse approximate inverse preconditioner (ISAI)
Stefan Haas: Simulation of the shallow water equations in the ExaHyPE-Engine with ADER-DG methods and dynamic adaptive mesh refinement
This is a Bachelor's Thesis submission talk advised by Michael Bader
ExaHyPE, an Exascale Hyperpolic PDE Engine, offers a game engine like solution to simulate hyperbolic partial differential equations, while tackling the challenges of future exascale supercomputers. In this thesis it is shown how to implement the shallow water equations in ExaHyPE as well as an additional Riemann solver to enable the wetting and drying of cells. It shows how much ExaHyPEs performance increases when using shared memory and distributed memory parallelisation and at which circumstances the best performance is achieved. The implementation of the solvers, especially the implementation of the additional Riemann solver, is then tested with two benchmarks. The results show that the implemented Riemann solver generates rather accurate results, but in the case of demanding problems it comes to its limits.
Keywords: ExaHyPE, ADER-DG, shallow water