Radial Basis Function Based Quadrature over Smooth Surfaces
Technical Report,01 Sep 2014,24 Mar 2016
AFIT WPAFB United States
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The numerical approximation of definite 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 of one dimension however, extension of integration of polynomial interpolants to two or more dimensions can be costly and unstable. 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 reduce computational complexity when generating quadrature weights for the particular node set. This thesis expands upon the same spherical quadrature method and applies it to an arbitrary smooth closed surface defined by a set of quadrature nodes and triangulation.
- Theoretical Mathematics