Hexagonal grid methods with applications to partial differential equations

Abstract

We consider in this work hexagonal grids for two-dimensional applications. A finite volume-based finite difference approach to solving Laplacian-related differential equations on hexagonal grids is developed. Both ordinary and compact hexagonal seven-point schemes are investigated. Theoretical properties of the associated linear algebraic systems are determined. These methods are applied to solve PDEs on both regular and curved domains, successfully exhibiting linear and spiral wave propagations in regular domains and curved wave in a reversed C-type domain.

Keywords:

• compact scheme
• hexagonal finite volume
• finite difference
• monodomain model
• reaction-diffusion

2010 AMS Subject Classifications:

• 65M06
• 65M08

Acknowledgements

The authors are grateful to Tunghai University, Providence University, Taichung Veterans General Hospital, and the National Science Council for continued laboratory support for a long period of time, partially under the grants NSC96-2115M126002 and TCVGH-PU968109.