Finite volume stiffness matrix for solving anisotropic cardiac propagation in 2-D and 3-D unstructured meshes

Abstract

The finite volume method (FVM) has been shown recently to be an effective method for discretizing the reaction-diffusion equations that govern wavefront propagation in anisotropic cardiac tissue, as it can naturally handle both complex geometries and no flux boundary conditions without the use of ghost nodes. This communication presents an alternative formulation of FVM for triangle and tetrahedral meshes using the concept of dual basis. An algorithm based on this form is given that leads to an efficient computation of the stiffness matrix, facilitating the incorporation of space adaptive schemes and time varying material properties into numerical simulations of cardiac dynamics.