Date of Award
3-24-2016
Document Type
Thesis
Degree Name
Master of Science in Applied Mathematics
Department
Department of Mathematics and Statistics
First Advisor
Jonah A. Reeger, PhD.
Abstract
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.
AFIT Designator
AFIT-ENC-MS-16-M-003
DTIC Accession Number
AD1010740
Recommended Citation
Watts, Maloupu L., "Radial Basis Function Based Quadrature over Smooth Surfaces" (2016). Theses and Dissertations. 249.
https://scholar.afit.edu/etd/249