# SC²S Colloquium - October 21, 2015

Date: |
October 21, 2015 |

Room: |
02.07.023 |

Time: |
3:00 pm, s.t. |

## Matthias Fischer: Parameter Estimation for the USHER algorithm Using Sparse Grids

In molecular dynamics simulation the usage of a macroscopic and microscopic scale can be advantageous. For the transition into the microscopic scale the insertion of molecules is a required task. This can be done by the USHER algorithm, that can be optimized through several parameters for different fluids. In this project we did a parameter study using sparse grids to discretize the parameter space and developed a tool to compute the optimal parameters for given fluids.

## Jean-Matthieu Gallard: Fast Multipole Method in MarDyn: FFT acceleration of the M2L phase

The Fast Multipole Method is a numerical technique allowing the calculation of long-ranged forces in the N-body problem with a time complexity of O(N). To do so, in a three-dimensional space, long-ranged particle to particle interactions taken into account via with Multipole expansion to Local expansion interactions (M2L). M2L can be seen as a convolution of two $(p+1) \times (2p+1)$ matrices, $p$ being the order of the expansions, which implies an expansive time complexity of O(p^4). However, in frequency domain the convolution becomes a simple entrywise product of complexity O(p^2), in accordance with the convolution theorem. This IDP focuses on implementing a Fast Fourier Transform acceleration of the M2L phase in the molecular dynamics simulation software ls1 mardyn. Taking into account certain symmetry relations in the expansions, an optimized code of the FFT can be used to improve space and time performances. The FFT acceleration is implemented using a pre- and post-processing scheme around the M2L phase and a memoized function to manage the transfer functions used during the M2L translations. Speedups of factor 2-9 were achieved for expansions with order p between 5 and 15.

## Raphael Schaller: Parallelization of a Non-Hydrostatic Shallow Water Model in Sam(oa)²

This talk discusses extension of the non-hydrostatic shallow water equations towards solving large problems on HPC architectures. We describe how the previous implementation of the non-hydrostatic shallow water equations in the PDE framework sam(oa)² is adapted in order to support parallel execution. Strong scaling as well as weak scaling results are presented, which show a parallel efficiency of about 96.8% for strong scaling on 512 cores and 90.1% for weak scaling on 8192 cores. To further improve performance, we examine and successfully demonstrate the application of the Conjugate Gradient Method - instead of the previously used Jacobi method - for solving the system of linear equations.