DISCRETE CYLINDRICAL AND SPHERICAL BESSEL TRANSFORMS IN NON-DIRECT PRODUCT REPRESENTATIONS

We extend the applicability of the discrete Bessel transform we have previously derived for the case of cylindrical or spherical symmetry. In the absence of symmetry we describe the fixed-grid algorithm which optimally deals with non-direct product representations. Exponential convergence is preserved as the number of grid points is increased. We thus provide new and efficient multidimensional pseudospectral schemes based on Laplacian eigenfunctions in cylindrical and spherical coordinates. The accuracy of the fixed-grid Bessel transform is demonstrated for the two- and three-dimensional harmonic oscillator.