Numerical simulation for unsteady helmholtz problems of anisotropic functionally graded materials

—The unsteady anisotropic Helmholtz type equation of spatially varying coefficients is considered in this study. The study is to find numerical solutions to initial boundary value problems governed by the equation. Such problems are relevant for anisotropic functionally graded materials. A mathematical analysis is used to transform the variable coefficient equation to a constant coefficient equation which is then Laplace-transformed (LT) to get a time-independent equation. The latest equation is then written as a boundary-only integral equation of a time-free fundamental solution. A boundary element method (BEM) which is derived from the integral equation and combined with the Stehfest formula for numerical Laplace transform inversion is then employed to find the numerical solutions. Some problems are considered. The combined LT-BEM is easy to implement. The results show that the numerical solutions obtained are accurate.