Numerical inversion of multivariate Laplace transforms using a parallel system

Abstract

This work was stimulated by investigations on Markow Renewal Processes. For finding analytic solutions (to compute the probabilities of certain states of the system) multivariate Laplace transforms can be used. Tables with correspondences of function and their transforms very rarely help to solve such problems.

In Chapter I number theoretical numerics are applied to compute the original function of a multivariate Laplace transform given. Starting with the complex multivariate inversion theorem the domain of integration is mapped onto the s-dimensional unit cube G_s. Using a periodization of the integrand new results concerning the vanishing of the multivariate Laplace transform in regard of the modified numerical inversion formula are shown.

In Chapter II two implementations are discussed: A method to implement a Manager-Worker Process (MWP) to reduce the idle times of the processors is presented and the tasks of the Manager and the Workers are defined. The numerical inversion using this method with STRAND⁸⁸ has been implemented on a heterogenous workstation net. The MWP provided a good load balancing. Another implementation with C-LINDA has been done on a Shared Memory MIMD system. We also implemented a kind of MWP. Numerical experiments have shown that the decomposition of the problem is sufficiently.