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

Abstract

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 βx values on the solutions, and the impact of the inhomogeneity and the isotropy of the materials to the solutions.

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