Energy Study of Monte Carlo and Quasi-Monte Carlo Algorithms for Solving Integral Equations

In the past few years the development of exascale computing technology necessitated to obtain an estimate for the energy consumption when large-scale problems are solved with different high-performance computing (HPC) systems. In this paper we study the energy efficiency of a class of Monte Carlo (MC) and Quasi-Monte Carlo (QMC) algorithms for a given integral equation using hybrid HPC systems. The algorithms are applied to solve quantum kinetic integral equations describing ultra-fast transport in quantum wire. We compare the energy performance of the algorithms using a GPU-based computer platform and CPU-based computer platform both with and without hyper-threading (HT) technology. We use SPRNG library and CURAND generator to produce parallel pseudo-random (PPR) sequences for the MC algorithms on CPU-based and GPU -based platforms, respectively. For our QMC algorithms Sobol and Halton sequences are used to produce parallel quasi-random (PQR) sequences. We compare the obtained results of the tested algorithms with respect to the given energy metric. The results of our study demonstrate the importance of taking into account not only scalability of the HPC intensive algorithms but also their energy efficiency. They also show the need for further optimisation of the QMC algorithms when GPU-based computing platforms are used.