A boundary-only element method for 2D unsteady diffusion convection reaction problems of trigonometrically graded anisotropic materials

Abstract A diffusion convection reaction (DCR) problem for anisotropic functionally graded materials (FGMs) is discussed in this paper to find numerical solutions by using a combined Laplace transform (LT) and boundary element method (BEM). The variable coefficients equation is transformed to a constant coefficients equation which is then Laplace-transformed so that the time variable vanishes. A purely boundary integral equation involving a time-free fundamental solution can then be derived and employed to find numerical solutions using a BEM. The results obtained are inversely transformed numerically using the Stehfest formula. The combined LT-BEM is easy to implement, efficient and accurate for solving numerically the problems.