Calculation of SPH and VSH Expansions
This method enables efficient and accurate spectral-element discretization of 3D scattering problems with spherical transparent boundary conditions, benefiting computational electromagnetics and acoustics.
The paper presents a spectrally accurate numerical method for computing spherical/vector spherical harmonic expansions from nodal values on a sphere, achieving high accuracy in reasonable time for 3D acoustic and electromagnetic scattering simulations.
We present in this paper a spectrally accurate numerical method for computing the spherical/vector spherical harmonic expansion of a function/vector field with given (elemental) nodal values on a spherical surface. Built upon suitable analytic formulas for dealing with the involved highly oscillatory integrands, the method is robust for high mode expansions. We apply the numerical method to the simulation of three-dimensional acoustic and electromagnetic multiple scattering problems. Various numerical evidences show that the high accuracy can be achieved within reasonable computational time. This also paves the way for spectral-element discretization of 3D scattering problems reduced by spherical transparent boundary conditions based on the Dirichlet-to-Neumann map.