Galerkin-Legendre spectral method for the 3D Helmholtz equation

A Galerkin-Legendre spectral method for the direct solution of Poisson and Helmholtz equations in a three-dimensional rectangular domain is presented, The method extends Jie Shen's algorithm for 2D problems by using the diago nalization of the three mass matrices in the three spatial directions and f ully exploits the direct product nature of the spectral approximation. The Dirichlet boundary values are taken into account by means of a discrete lif ting performed in three subsequent steps and built upon Gauss-Legendre quad rature points. A few numerical tests illustrate the accuracy and efficiency of the method. (C) 2000 Academic Press.