Boundary value problems governed by Helmholtz equation for anisotropic trigonometrically graded materials: A boundary element method solution

Abstract

Abstract Trigonometrically graded media of anisotropic diffusion coefficient are under consideration. Boundary value problems (BVPs) of such kind of media, governed by a Helmholtz type equation, are solved numerically using a boundary element method (BEM). A technique of transforming the variable coefficient governing equation to a constant coefficient equation is utilized for deriving a boundary integral equation. Some particular problems are considered to illustrate the application of the BEM. The results show convergence, accuracy and consistency between the scattering and flow solutions. The results also show efficiency of the BEM procedure for producing the solutions in a short elapsed computation time length. Moreover the results indicate the effect of large wave number on the accuracy and the impact of the inhomogeneity and anisotropy of the material on the solutions.