Parallel block interface domain decomposition methods for the 2D convection–diffusion equation

Abstract

In this paper, a new block interface domain decomposition method (BI-DDM) with non-overlapping subdomains for the numerical solution of a two-dimensional convection–diffusion equation is presented. The block interface formulation is derived from the idea of using small groups of a certain number of mesh points where this group is treated explicitly similar to the way a single point is treated in the point method. The BI-DDM is incorporated with a correction phase which is able to economize further on the computing cost. The performance analysis of this method on several recently developed group iterative schemes implemented on a message-passing architecture are presented and discussed.

Keywords:

• explicit group method
• domain decomposition
• message-passing interface
• convection–diffusion
• parallel algorithm

2010 AMS Subject Classifications::

• 65N06
• 65Y05
• 65N55

Acknowledgements

The authors acknowledge the USM School of Mathematical Sciences KPI Incentive Grant and the Fundamental Research Grant Scheme (203/PMATHS/6711188) for the completion of this article.