On the effect of the material’s anisotropy: a numerical investigation for the modified Helmholtz problems of homogeneous media

This paper focuses on the study of the effect of the anisotropy of a medium in question to the values of the dependent variable. Boundary value problems governed by the two-dimensional modified Helmholtz equation for anisotropic media are considered. Specifically, it is the diffusion or conduction process which is assumed to be anisotropic. The standard boundary element method is used to find numerical solutions to the problems. The solutions show that the anisotropy of the medium causes certain effects on the solution. Therefore the anisotropy of the medium should be taken into account in the modeling and computation for the solution, specifically for experimental studies.