GPU Optimization of Pseudo Random Number Generators for Random Ordinary Differential Equations

Solving differential equations with stochastic terms involves a massive use of pseudo random numbers. We present an application for the simulation of wireframe buildings under stochastic earthquake excitation. The inherent potential for vectorization of the application is used to its full extent on GPU accelerator hardware. A representative set of pseudo random number generators for uniformly and normally distributed pseudo random numbers has been implemented, optimized, and benchmarked. The resulting optimized variants outperform standard library implementations on GPUs. The techniques and improvements shown in this contribution using the Kanai-Tajimi model can be generalized to other random differential equations or stochastic models as well as other accelerators.