The method of fundamental solutions for Helmholtz-type equations in composite materials

In this paper, we introduce and develop the method of fundamental solutions (MFS) for solving Helmholtz-type elliptic partial differential equations in composite materials. This study builds upon the previous developments and applications of the MFS to linear and nonlinear heat conduction, elasticity, and functionally graded composite layered materials. Numerical results are presented and discussed for four examples involving both the modified Helmholtz and the Helmholtz equations in two-dimensional or three-dimensional, bounded or unbounded, smooth or non-smooth composite domains. It was found that the method produces numerical results which are in good agreement with the analytical solutions, where available.