A parallel partition of unity method for the time-dependent convection-diffusion equations

Abstract

Purpose

The purpose of this paper is to propose a parallel partition of unity method to solve the time-dependent convection-diffusion equations.

Design/methodology/approach

This paper opted for the time-dependent convection-diffusion equations using the finite element method and the partition of unity method.

Findings

This paper provides one efficient parallel algorithm which reaches the same accuracy as the standard Galerkin method (SGM) but saves a lot of computational time.

Originality/value

In this paper, a parallel partition of unity method is proposed for the time-dependent convection-diffusion equations. At each time step, the authors only need to solve a series of independent local sub-problems in parallel instead of one global problem.

Citation

Du, G. and Hou, Y. (2015), "A parallel partition of unity method for the time-dependent convection-diffusion equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 8, pp. 1947-1956. https://doi.org/10.1108/HFF-09-2014-0277