Gimbutas, Zydrunas; Veerapaneni, Shravan A fast algorithm for spherical grid rotations and its application to singular quadrature. (English) Zbl 1285.65089 SIAM J. Sci. Comput. 35, No. 6, A2738-A2751 (2013). Summary: We present a fast and accurate algorithm for evaluating singular integral operators on smooth surfaces that are globally parametrized by spherical coordinates. Problems of this type arise, for example, in simulating Stokes flows with particulate suspensions and in multiparticle scattering calculations. For smooth surfaces, spherical harmonic expansions are commonly used for geometry representation and the evaluation of the singular integrals is carried out with a spectrally accurate quadrature rule on a set of rotated spherical grids. We propose a new algorithm that interpolates function values on the rotated spherical grids via hybrid nonuniform fast Fourier transforms. The algorithm has a small complexity constant, and the cost of applying the quadrature rule is nearly optimal \(\mathcal{O}(p^4\log p)\) for a spherical harmonic expansion of degree \(p\). Cited in 1 ReviewCited in 16 Documents MSC: 65R20 Numerical methods for integral equations 45P05 Integral operators 33C55 Spherical harmonics 65T50 Numerical methods for discrete and fast Fourier transforms 65T40 Numerical methods for trigonometric approximation and interpolation Keywords:spherical harmonics; boundary integral equations; singular quadrature; interpolation; numerical example; singular integral operator; spherical harmonic expansion; algorithm; nonuniform fast Fourier transform Software:NFFT PDFBibTeX XMLCite \textit{Z. Gimbutas} and \textit{S. Veerapaneni}, SIAM J. Sci. Comput. 35, No. 6, A2738--A2751 (2013; Zbl 1285.65089) Full Text: DOI