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Volume 6, Issue 3
Fast Spectral Collocation Method for Surface Integral Equations of Potential Problems in a Spheroid

Zhenli Xu & Wei Cai

Commun. Comput. Phys., 6 (2009), pp. 625-638.

Published online: 2009-06

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  • Abstract

This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid. The layer densities are approximated by a spectral expansion of spherical harmonics and the spectral collocation method is then used to solve surface integral equations of potential problems in a spheroid. With the proposed technique, the computation cost of collocation matrix entries is reduced from O(M2N4) to O(MN4), where Nis the number of spherical harmonics (i.e., size of the matrix) and M is the number of one-dimensional integration quadrature points. Numerical results demonstrate the spectral accuracy of the method.

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@Article{CiCP-6-625, author = {}, title = {Fast Spectral Collocation Method for Surface Integral Equations of Potential Problems in a Spheroid}, journal = {Communications in Computational Physics}, year = {2009}, volume = {6}, number = {3}, pages = {625--638}, abstract = {

This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid. The layer densities are approximated by a spectral expansion of spherical harmonics and the spectral collocation method is then used to solve surface integral equations of potential problems in a spheroid. With the proposed technique, the computation cost of collocation matrix entries is reduced from O(M2N4) to O(MN4), where Nis the number of spherical harmonics (i.e., size of the matrix) and M is the number of one-dimensional integration quadrature points. Numerical results demonstrate the spectral accuracy of the method.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7697.html} }
TY - JOUR T1 - Fast Spectral Collocation Method for Surface Integral Equations of Potential Problems in a Spheroid JO - Communications in Computational Physics VL - 3 SP - 625 EP - 638 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7697.html KW - AB -

This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid. The layer densities are approximated by a spectral expansion of spherical harmonics and the spectral collocation method is then used to solve surface integral equations of potential problems in a spheroid. With the proposed technique, the computation cost of collocation matrix entries is reduced from O(M2N4) to O(MN4), where Nis the number of spherical harmonics (i.e., size of the matrix) and M is the number of one-dimensional integration quadrature points. Numerical results demonstrate the spectral accuracy of the method.

Zhenli Xu & Wei Cai. (2020). Fast Spectral Collocation Method for Surface Integral Equations of Potential Problems in a Spheroid. Communications in Computational Physics. 6 (3). 625-638. doi:
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