Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids

作者：Wang, Bo; Wang, Li-Lian^*; Xie, Ziqing

来源：Advances in Computational Mathematics, 2018, 44(3): 951-985.

DOI：10.1007/s10444-017-9569-1

• Spherical harmonics
• Vector spherical harmonics
• Spectral elements
• Analytic formulas
• High mode expansions
• Multiple scattering
• Helmholtz equation
• Maxwell equations
• Far-field scattering waves

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.

• 出版日期2018-6
• 单位南阳理工学院; 湖南师范大学