Hexagonal grid methods with applications to partial differential equations

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 prope...

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Bibliographic Details
Published in:International journal of computer mathematics 2014-09, Vol.91 (9), p.1986-2009
Main Authors: Lee, D., Tien, H.C., Luo, C.P., Luk, H.-N.
Format: Article
Language:English
Subjects:
Algebra
compact scheme
Curved
Differential equations
Dimensional analysis
finite difference
Geometry
Grid method
hexagonal finite volume
Laplace transforms
Linear algebra
Mathematical analysis
Mathematical problems
monodomain model
Partial differential equations
reaction-diffusion
Two dimensional
Wave propagation
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Summary: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.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2013.864392