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SC²S Colloquium - June 1, 2017

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Date: June 1, 2017
Room: 02.07.023
Time: 04:00 pm, s.t.

Katrin Degel: Sparse grid refinement for multiple classes

With the help of sparse grids, high dimensional data sets are classified. The classification uses the grid points to approximate the density functions for the given classes. Based on the problem, grid points are added in areas of interest. Those are regions where classes overlap or have common boundaries. When doing a pairwise comparision of classes, the execution time increases quadratically with the number of classes. Thus, an adaptation to the zero-crossing based refinement is made to reduce the class dependend scaling. In this work, the sparse grid toolbox of SG++ is expanded by a refinement functor, created to optimize the classification task with multiple classes. The newly introduced datastructures and algorithms are presented and an overview over the parameters is given. An evaluation is provided to compare the implemented refinement functor with the existing refinement functors. The evaluation is based on a four-dimensional data set, containing around two million data points in three classes.

Walter Arthur Simson IV: A practical approach to walking on Spheres with GPUs,

The task of solving high dimensional partial differential equations numerically can be challenging and time consuming. Nevertheless, the solutions of these problems can be of the utmost importance, for instance in the fields of nuclear fusion and modern finance. In order to solve these math problems, we need highly powerful and parallel comput- ers to assist us. As computing resources become more powerful, programming highly parallel computing systems becomes more complex. We intend to show that high dimen- sional PDEs can be efficiently solved running the Random Walk on Spheres algorithm on Graphical Processing Units (GPU). To do this, we built a proof of concept to solve a classic exemplary PDE, compared running time on the GPU to CPU running time and calculated the performance gains. In this work, we we had great success proving the efficacy of this approach and measured performance gains of 600 times for 128 dimensional case. Even higher performance gains are expected in higher dimensions. This work strives to show the applicability of Random Walk on Spheres in solving high dimensional Partial Differen- tial Equations, and serve as a guideline for future work in order to attain highly optimized solvers.

Amir Raoofy: Design and Implementation of a semi-implicit solver for the simulation of overland flows on high performance computers

The aim of this thesis is to present a design and implementation of an existing semi-implicit numerical method for overland flows with hydrostatic pressure assumption on modern high performance computers and study the properties of the semi-implicit methods for overland flows in a parallel computer. In order to address the parallelization, domain decomposition in the two-dimensional grid is suggested and used as it is a simple strait-forward parallelization technique, and as we discuss, it is a suitable method for study of the semi-implicit methods due to the properties and the sub-steps of the algorithm of this numerical method. We implemented and a three-dimensional shallow water solver for overland flows based on the presented design that is able to use a build-in Jacobi solver as well as the iterative solvers in PETSc. In order to validate the solver results and to study the possibilities and the behaviors of the solver, different simulation scenarios are introduced, implemented and tested including the dam break and gravity wave propagation. We have studied the properties of the solver such as the convergence rates and time complexity of the solver using these scenarios. In order to analyze the performance of the solver, Linux cluster and CoolMUC2 are used and the weak scaling behavior of the solver on this cluster is presented and analyzed. At the end a conclusion based on our experiences with the semi-implicit method and the parallel implementation of the presented numerical approach is made and the possibilities for future works and later extensions are discussed.