A Fourier–Wachspress method for solving Helmholtz’s equation in three-dimensional layered domains

In this paper, we present a fast direct method for solving Poisson’s or Helmholtz’s equation in three-dimensional layered domains. The method combines a Fourier method for two dimensions and a variant of Wachspress’s method in the third dimension. The resulting scheme is capable of efficiently creating solutions that are highly accurate even when the coefficients defining the layered structure are discontinuous or extreme mesh refinement is used.