title: Numerical quadrature over smooth, closed surfaces.
abstract: The numerical approximation of definite integrals, or quadrature, often involves the construction of an interpolant of the integrand and its subsequent integration. In the case of one dimension it is natural to rely on polynomial interpolants. However, their extension to two or more dimensions can be costly and unstable. An efficient method for computing surface integrals on the sphere is detailed in the literature (Reeger & Fornberg 2016Stud. Appl. Math.137, 174-188. (doi:10.1111/sapm.12106)). The method uses local radial basis function interpolation to reduce computational complexity when generating quadrature weights for any given node set. This article generalizes this method to arbitrary smooth closed surfaces.
authors.affiliation: Department of Mathematics and Statistics , Air Force Institute of Technology, 2950 Hobson Way , Wright-Patterson Air Force Base, OH 45433-7765, USA.
authors.forename: J A
authors.identifier: 0000-0003-3211-7070
authors.initials: JA
authors.lastname: Reeger
authors.affiliation: Department of Applied Mathematics , University of Colorado , 526 UCB, Boulder, CO 80309, USA.
authors.forename: B
authors.initials: B
authors.lastname: Fornberg
authors.affiliation: Department of Mathematics and Statistics , Air Force Institute of Technology, 2950 Hobson Way , Wright-Patterson Air Force Base, OH 45433-7765, USA.
authors.forename: M L
authors.initials: ML
authors.lastname: Watts
keywords: quadrature; radial basis function-finite differences; radial basis functions; surface integral