SC²S Colloquium - May 22, 2017

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Date: May 22, 2017
Room: 01.09.014
Time: 10:30 am, s.t.

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.