TY - JOUR
T1 - Fast Spectral Collocation Method for Surface Integral Equations of Potential Problems in a Spheroid
AU - Zhenli Xu & Wei Cai
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 - <p style="text-align: justify;">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(M<sup>2</sup>N<sup>4</sup>) to
O(MN<sup>4</sup>), where N<sup>2&nbsp;</sup>is 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.</p>