A Parallel Solver of Diffusion-Advection Equations

Project team

Research Objectives

One of the main challenges in the field of computational intensive numerical applications is the development of methods for solving time dependent diffusion-advection equations in parallel. This problem has been recently examined intensively because of its crucial importance in modelling many physical and chemical processes, e.g. the transport of air pollutants in the sphere.
Zoltan Horvath and I are working on the development of a novel parallel method for the numerical solution of initial value problems for systems of ordinary differential equations which arise from semidiscretization of partial differential equations describing diffusion and advection of some species. This method relies on splitting techniques developed by Z. Horvath and is very promising in several ways.

Firstly, these techniques allow the computational work to be divided into a large number of subcomputations which can be executed efficiently in parallel. Secondly, initial experiments for 1D linear test problems showed that the numerical properties of the method (such as stability and accuracy) are comparable to convential sequential methods. Moreover, a qualitative property of the numerical solution, the preservation of nonnegativity of the initial data independently of the time step size, is, up till now, only obtained by these techniques, providing a higher order of accuracy.

This research is supported by the Netherlands Organisation for Scientific Research (NWO) under Grant No. R 62-440.

Collaborations

Close collaboration exists with Dr. Z. Horvath from the Szechenyi Istvan College, Gyor, Hungary.

Intended results, deliverables

Design and implementation of a parallel solver of diffusion-advection equations for a wide range of shared and distributed memory architectures.

Timetable

Starting date: October 1994
Ending date: ...
Last modified on July 2, 1996 by Lex Wolters.