Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids
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 oscillator...
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sg-ntu-dr.10356-1437002020-09-17T05:34:12Z Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids Wang, Bo Wang, Li-Lian Xie, Ziqing School of Physical and Mathematical Sciences Science::Mathematics Spherical Harmonics Vector Spherical Harmonics 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. 2020-09-17T05:34:12Z 2020-09-17T05:34:12Z 2018 Journal Article 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 1019-7168 https://hdl.handle.net/10356/143700 10.1007/s10444-017-9569-1 3 44 951 985 en Advances in Computational Mathematics © 2018. Springer Nature. All rights reserved. |
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Science::Mathematics Spherical Harmonics Vector Spherical Harmonics Wang, Bo Wang, Li-Lian Xie, Ziqing Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids |
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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. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Wang, Bo Wang, Li-Lian Xie, Ziqing |
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Article |
author |
Wang, Bo Wang, Li-Lian Xie, Ziqing |
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Wang, Bo |
title |
Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids |
title_short |
Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids |
title_full |
Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids |
title_fullStr |
Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids |
title_full_unstemmed |
Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids |
title_sort |
accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids |
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2020 |
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https://hdl.handle.net/10356/143700 |
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1681056078765228032 |