Radial Basis Function Based Quadrature over Smooth Surfaces

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Mar 24, 2016
Accession Number
AD1010740

Entities

People

  • Maloupu L. Watts

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Air Force
  • Computational Complexity
  • Coordinate Systems
  • Department Of Defense
  • Differential Equations
  • Equations
  • Geometric Forms
  • Geometry
  • Governments
  • Linear Systems
  • Mathematics
  • Numerical Quadrature
  • Partial Differential Equations
  • Scalar Functions
  • Three Dimensional
  • Two Dimensional
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)