Volume 13, Issue 4

We present in this paper a GPU-based strategy that allows a fast reuse of paths in the context of shooting random walk applied to radiosity. Given an environment with diffuse surfaces, we aim at computing a basis of n radiosity solutions, corresponding to n light-source positions. Thanks to the reuse, paths originated at each of the positions are used to also distribute power from every other position. The visibility computations needed to make possible the reuse of paths are drastically accelerated using graphic hardware, resulting in a theoretical speed-up factor of n with regard to the computation of the independent solutions. Our contribution has application to the fields of interior design, animation, and videogames.

Approximate evaluation of mathematical expectations of nonlinear functionals of solutions to stochastic differential equations is considered. The approach based on interpolation of the coefficient functions of the equation is extended to the case of equations including integrals with respect to Poisson random measure and stochastic Wiener integral.

In this work, formulas for approximate evaluation of matrix valued functional integrals are constructed. These formulas are based on exact results for the matrix valued integrals of functional polynomials and the Monte Carlo method.

The Boltzmann equation in presence of boundary and initial conditions, which describes the general case of carrier transport in microelectronic devices is analysed in terms of Monte Carlo theory. The classical Ensemble Monte Carlo algorithm which has been devised by merely phenomenological considerations of the initial and boundary carrier contributions is now derived in a formal way. The approach allows to suggest a set of event-biasing algorithms for statistical enhancement as an alternative of the population control technique, which is virtually the only algorithm currently used in particle simulators. The scheme of the self-consistent coupling of Boltzmann and Poisson equation is considered for the case of weighted particles. It is shown that particles survive the successive iteration steps.