Universal Quadratures for Boundary Integral Equations on Two-Dimensional Domains with Corners

Abstract

We describe the construction of a collection of quadrature formulae suitable for the efficient discretization of certain boundary integral equations on a very general class of two-dimensional domains with corner points. The resulting quadrature rules allow for the rapid high accuracy solution of Laplace's equation and the Helmholtz equation on such domains. Our approach can be adapted to many other boundary value problems as well as to the case of surfaces with singularities in three dimensions. The performance of the quadrature rules is illustrated with several numerical examples.

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Document Details

Document Type
Technical Report
Publication Date
Nov 24, 2009
Accession Number
ADA555117

Entities

People

  • I. Sammis
  • J. Bremer
  • Vladimir Rokhlin

Organizations

  • Yale University

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Computations
  • Construction
  • Curvature
  • Equations
  • Geometry
  • Helmholtz Equations
  • Integral Equations
  • Integrals
  • Linear Systems
  • Mathematics
  • Polynomials
  • Precision
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.