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 2016 Stud. 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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Oct 01, 2016
- Source ID
- 10.1098/rspa.2016.0401
Entities
People
- B. Fornberg
- Jonah Reeger
- M. L. Watts
Organizations
- Air Force Institute of Technology
- United States Department of Defense
- University of Colorado