A fast method for solving three-dimensional arbitrarily shaped inclusions in a half space

This paper presents a fast method for solving the problem of three-dimensional arbitrarily shaped inclusions in an isotropic half space. The solution utilizes the closed-form solution for a cuboidal inclusion in an infinite space by breaking up the arbitrarily shaped inclusions into multiple cuboids. A combination of three-dimensional and two-dimensional fast Fourier transform algorithms is applied to evaluate the solution. Both theoretical estimates and computational tests demonstrate that the present method can achieve significant computational efficiency as well as effective data space reduction. Numerical results are also presented that show the applicability of the method to available solutions for error analysis and to new solutions.