A Simple Algorithm for Obtaining Nearly Optimal Quadrature Rules for NURBS-based Isogeometric Analysis

Abstract

We develop new quadrature rules for Isogeometric Analysis based on the solution of a local nonlinear problem. A simple and robust algorithm is developed to determine the rules which are exact for important B-Spline spaces of uniform and geometrically stretched knot spacings. We consider both periodic and open knot vector configurations and illustrate the efficiency of the rules on selected boundary value problems. We find that the rules are almost optimally efficient, but much easier to obtain than optimal rules, which require the solution of global nonlinear problems that are often ill-posed.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 05, 2012
Accession Number
ADA555391

Entities

People

  • A. Reali
  • F. Auricchio
  • F. Calabro
  • Giancarlo Sangalli
  • Thomas J.R. Hughes

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Boundary Layer
  • Boundary Value Problems
  • Computational Science
  • Computations
  • Computer-Aided Design
  • Construction
  • Convergence
  • Engineering
  • Equations
  • Fluid Dynamics
  • Geometry
  • Military Research
  • Precision
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers