Solving anisotropic elliptic and parabolic equations by a meshless method: simulation of the electrical conductivity of a tissue

Abstract

In this paper, the extension of the generalized finite difference method to the solution of anisotropic elliptical and parabolic partial differential equations is given in the case of considering two space dimensions. The explicit finite difference formulae and the criterion of stability for the anisotropic parabolic equations are given. The stability condition has been expressed in function of the coefficients of the star equation for irregular clouds of nodes. Various anisotropic cases of simulation of cardiac tissue, including elliptic and parabolic equations, have been solved, and the results show the accuracy of the method.

Keywords:

• generalized finite difference
• anisotropic
• simulation
• tissue

2000 AMS Subject Classifications::

• 65M06
• 65M12
• 92B99

Acknowledgements

The authors acknowledge the support from Ministerio de Ciencia e Innovación of Spain, project CGL2008–01757/CLI.