A Computational Study on Unsteady Anisotropic Helmholtz Type Equation of Quadratically Varying Coefficients.

This paper explores the unsteady Helmholtz type equation with quadratically varying coefficients for anisotropic inhomogeneous media. The paper proposes using a combined Laplace transform and boundary element method to find numerical solutions to problems governed by the equation. The variable coefficients equation is transformed into a constant coefficients equation which is then written in a boundary integral equation involving a time-free fundamental solution. The boundary-only integral equation is used with a standard boundary element method to find the numerical solutions. The results are then transformed numerically using the Stehfest formula to get solutions in the time variable. The paper concludes that the combined Laplace transform and boundary element method is both easy to implement and accurate, as demonstrated by problems related to anisotropic quadratically graded media. [ABSTRACT FROM AUTHOR]