Fast Spectral Collocation Method for Surface Integral Equations of Potential Problems in a Spheroid (Communications in Computational Physics, 2009)
This paper proposes a new technique to speed up the computation of thematrix of spectral collocation discretizations of surface single and double layer operatorsover a spheroid. The layer densities are approximated by a spectral expansionof spherical harmonics and the spectral collocation method is then used to solve surfaceintegral equations of potential problems in a spheroid. With the proposed technique,the computation cost of collocation matrix entries is reduced from O(M2N4) toO(MN4), where N2 is the number of spherical harmonics (i.e., size of the matrix) andM is the number of one-dimensional integration quadrature points. Numerical resultsdemonstrate the spectral accuracy of the method.