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Title: Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids
Authors: Wang, Bo
Wang, Li-Lian
Xie, Ziqing
Keywords: Science::Mathematics
Issue Date: 2018
Source: Wang, B., Wang, L.-L., & Xie, Z. (2018). Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids. Advances in Computational Mathematics, 44(3), 951-985. doi:10.1007/s10444-017-9569-1
Journal: Advances in Computational Mathematics
Abstract: 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.
ISSN: 1019-7168
DOI: 10.1007/s10444-017-9569-1
Rights: © 2018. Springer Nature. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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