Numerical solutions to anisotropic BVPs for quadratically graded media governed by a Helmholtz equation

Abstract

A Boundary Element Method (BEM) is used for obtaining solutions to anisotropic quadratically graded media boundary value problems (BVPs) governed by a Helmholtz type equation. 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 the convergence, consistency, and accuracy of the BEM solutions.