The parallel implementation of forward-reverse estimator

Abstract

Last several years the ship accidents caused the serious ecological catastrophes in the seaside of different countries. To prevent or, at least, reduce the possible damage due to accidents we need to develop efficient and accurate model for the simulation of the pollution spreading. The movement of the pollutant can be modeled by using a random walk model. Here the trajectory of a particle of the pollutant is simulated with the help of the appropriate system of the stochastic differential equations. By averaging the positions of many particles the concentration of the pollutant can be found. For a number of application,it is not necessary to simulate the concentration in the whole domain of the problem For these kind of problem the forward- reverse estimator can be applied. This estimator has recently been introduced by Milstein, Schoenmakers and Spokoiny and is based on realizations of original forward system and also on realizations of reverse time system derived from original forward one. This approach allows to compute the concentration of the pollutant in certain region efficiently without solving the complete simulation problem. Because of the independence of movement of particles random walk models can be easily parallelized. In this paper we considered the parallelization of the forward-reverse estimator based on the particle decomposition. Several approaches are proposed and their advantages, disadvantages and efficiency are discussed. The parallel version of the forward-reverse method is applied for the simulation of the pollution spreading along the Dutch seaside. For this model we investigate the efficiency of the parallel algorithm. The result show that the efficiency of the parallelization is very high, especially for a large size of realizations.