A GPU domain decomposition solution for spectral stochastic finite element method

Abstract

In intrusive methods for the stochastic analysis of engineering systems, the solution of the stochastic partial differential equations leads to an augmented algebraic system of equations, with respect to the corresponding deterministic problem. The solution of this augmented system can become quite challenging or even impossible due to the increased computational resources and effort required, especially in large-scale problems with large parameter variability. Recent developments in computer hardware regarding graphics processing units (GPU)-accelerated computing have been proven very promising due to their advanced capabilities and have been used in a number of scientific fields in order to enhance the solution of computationally high demanding problems. In this work, the benefits achieved with the exploitation of the GPU capabilities are demonstrated, in addressing intrusive stochastic mechanics problems where the solution of the resulting finite element algebraic equations is performed with the dual domain decomposition method, implementing specifically tailored preconditioners. The results show a significant enhancement of the spectral stochastic finite element method in terms of computational performance as well as of the consumed energy efficiency when applying the proposed methodology.