An Algorithm to Evaluate Spectral Densities of High-Dimensional Stationary Diffusion Stochastic Processes with Non-linear Coefficients: The General Scheme and Issues on Implementation with PVM

摘要

The present work deals with spectral-density matrix of the stationary diffusion stochastic process with non-linear coefficients (i.e. drift vector and diffusion matrix) in the case as number of variables of the process is high, i.e. is much greater than a few units. This is an important topic in modern microelectronics and other applied fields associated with non-linear fluctuations in high-dimensional systems. A general scheme for the algorithm to evaluate the above matrix for realistic computing expenses is proposed. This algorithm applies the Monte Carlo method for multifold integrals. An implementation with the Parallel Virtual Machine (PVM) software environment is discussed. To reduce the corresponding message-passing time overheads, the initial-and-final-only-messages (IFOM) technique should be applied. It is shown that the IFOM approach enables to keep the parallelization efficiency at the level of 80-90% even if many tens (or more) processors are involved.