NUMERICAL COMPUTATION OF THE LAPLACE-BELTRAMI OPERATOR ON THE SPHERE

Abstract

We propose a method for computation of the Laplace-Beltrami operator of a spherical function. It is proved that differentiation may be replaced by integration with a kernel derived from the Poisson kernel, followed by a limit computation. Theoretical results show uniform convergence, but in practice, limiting process is difficult to be performed and it turns out that the error is too big. Numerical experiments show that under assumption that the test function is bandlimited, computation of its Laplace- Beltrami operator can be performed via integration with a proper polynomial kernel.