Date of Award
Master of Science in Applied Mathematics
Department of Mathematics and Statistics
Jonah A. Reeger, PhD.
The numerical approximation of denite integrals, or quadrature, often involves the construction of an interpolant of the integrand and subsequent integration of the interpolant. It is natural to rely on polynomial interpolants in the case ofone dimension; however, extension of integration of polynomial interpolants to two or more dimensions can be costly andunstable. A method for computing surface integrals on the sphere is detailed in the literature (Reeger and Fornberg,Studies in Applied Mathematics, 2016). The method uses local radial basis function (RBF) interpolation to reducecomputational complexity when generating quadrature weights for the particular node set. This thesis expands upon thesame spherical quadrature method and applies it to an arbitrary smooth closed surface dened by a set of quadraturenodes and triangulation.
DTIC Accession Number
Watts, Maloupu L., "Radial Basis Function Based Quadrature over Smooth Surfaces" (2016). Theses and Dissertations. 249.