Parallel finite difference solution of general inhomogeneous anisotropic bio-electrostatic problems

Finite difference solution of bio-electrostatic problems have been limited mainly to systems where the conductivity is orthotropic, i.e., a strictly diagonal conductivity tensor. This in turn has limited the use of the finite difference technique in modeling the detailed structure of various muscles, where the fibers can be in arbitrary directions and an accurate representation demands a non-diagonal conductivity tensor. Here, the authors describe a new three-dimensional finite difference formulation that is valid for solving the governing Laplace equation in structures with an inhomogeneous and non-diagonal conductivity tensor. In addition, a data parallel computer is used in the finite difference implementation to provide the memory and reduction in solution time for solving large problems. The finite difference algorithm will be described together with its parallel implementation, and numerical results is presented.