The Intel MIC architecture is one of the main processor architectures used for the production of computational accelerators. Increasing energy and cost-effciency of accelerators is one important option for building new HPC systems. However, the effective use of accelerators requires careful optimization on all stages of the algorithm and use of appropriate parallelization approaches. In the domain of statistical methods the quasi-Monte Carlo methods present distinct challenges when thousands of computational cores are to be involved in a computation. In this paper we describe in detail and study the performance of algorithms for generating some popular low-discrepancy sequences, aimed at devices with Intel MIC architecture. By leveraging the powerful vector instructions of the Intel MIC architecture to process many coordinates of the sequences in parallel, we obtain fast implementations that can be plugged-in in any parallel quasi-Monte Carlo computation. We present extensive numerical and timing results that demonstrate the benefit of our algorithms and their parallel effciency. The effects of using hyperthreading are also studied. The generation routines are provided under the GPL.

This paper studies generator sensitivity of some variance reduction Monte Carlo methods (MCMs) with acceptance‐rejection for approximate calculation of multiple integrals. This investigation is important basis for the development of the grid application Monte Carlo Sensitivity Analysis for Environmental Systems in the framework of the SEE‐GRID‐SCI project. Monte Carlo are among the most widely used methods in real simulations. These methods can be considered as methods for computing an integral in the unit cube of an appropriate dimension, called the constructive dimensionality of the method. Since its worst‐case convergence rate of O(N −1/2 ) does not depend on the dimension of the integral, Monte Carlo is sometimes the only viable method for a wide range of high‐dimensional problems. Many studies show that the outcome of the simulation may be sensitive to the random generators being used, which means that obtaining unbiased estimates requires careful selection of the random generators. The random number generators based on physical events present an important option in this regard. In this paper we study the sensitivity of several variance reduction Monte Carlo methods: importance sampling, smoothed importance sampling, weighted uniform sampling and crude Monte Carlo, to different type of generators: Quantum Random Bit Generator, pseudorandom generators and quasi‐random sequences. Extensive numerical tests of several test integrals are presented.