Parallel Importance Separation for Multiple Integrals and Integral Equations

摘要

In this paper we present error and performance analysis of a Monte Carlo variance reduction method for solving multidimensional integrals and integral equations. This method, called importance separation, combines the idea of separation of the domain into uniformly small subdomains with the approach of importance sampling. The importance separation method is originally described in our previous works, here we generalize our results and discuss the performance in comparison with crude Monte Carlo and importance sampling. Based on our previous investigation we propose efficient parallelizations of the importance separ ration method. Numerical tests implemented on PowerPC cluster using MPI are provided. The considered algorithms are carried out using pseudorandom numbers.