Isogeometric Analysis of Boundary Integral Equations

Abstract

Isogeometric analysis is applied to boundary integral equations corresponding to boundary-value problems governed by Laplace's equation. It is shown that the smoothness of geometric parameterizations central to computer-aided design can be exploited for regularizing integral operators. As a result one obtains high-order collocation methods based on superior approximation and numerical integration schemes and well-conditioned systems of linear algebraic equations. It is demonstrated that the proposed approach allows one to solve boundary-value problems with an accuracy close to machine precision.

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Document Details

Document Type
Technical Report
Publication Date
Apr 21, 2015
Accession Number
ADA620024

Entities

People

  • Gregory J. Rodin
  • Matthias Taus
  • Thomas J.R. Hughes

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Boundaries
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Computer-Aided Design
  • Equations
  • Fluid Mechanics
  • Gaussian Quadrature
  • Geometry
  • Integral Equations
  • Integrals
  • Linear Algebraic Equations
  • Mechanics
  • Numerical Integration
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)