Numerical simulation of two-dimensional modified Helmholtz problems for anisotropic functionally graded materials

In this paper we consider the modified Helmholtz type equation governing 2D-boundary value problems
for anisotropic functionally graded materials (FGMs) with Dirichlet and Neumann boundary conditions.
The persistently spatially changing diffusion and leakage factor coefficients involved in the governing
equation indicate the inhomogeneity of the material under consideration. And the anisotropic diffusion
coefficients indicate the material’s anisotropy. Some particular examples of problems are solved numerically
using a boundary element method (BEM). The results show the accuracy and consistency of the
numerical solutions, the effect of the coefficient bðxÞ values on the solutions, and the impact of the inhomogeneity
and the isotropy of the materials to the solutions