Parallel Quasirandom Applications on Heterogeneous Grid

Abstract

In this paper we present error and performance analysis of quasi-Monte Carlo
algorithms for solving multidimensional integrals (up to 100 dimensions)
on the grid using MPI.
We take into account the fact that the Grid is a potentially
heterogeneous computing environment, where the user does not know
the specifics of the target architecture. Therefore parallel
algorithms should be able to adapt to this heterogeneity,
providing automated load-balancing. Monte Carlo algorithms
can be tailored to such environments, provided parallel
pseudorandom number generators are available. The use
of quasi-Monte Carlo algorithms poses more difficulties.
In both cases the efficient implementation of the algorithms
depends on the functionality of the corresponding packages for
generating pseudorandom or quasirandom numbers. We propose
efficient parallel implementation of the Sobol sequence for
a grid environment and we demonstrate numerical experiments on a heterogeneous grid.
To achieve high parallel efficiency we use a newly developed special grid service
called Job Track Service which provides efficient management
of available computing resources through reservations.