A Fast Algorithm for the Numerical Evaluation of Conformal Mappings.

Abstract

An algorithm is presented for the construction of conformal mappings from arbitrary simply-connected regions in the complex plane onto the unit disk. The algorithm is based on a combination of the Kerzman-Stein integral equation and the Fast Multipole Method for the evaluation of Cauchy-type integrals. Previously published methods of this type have an asymptotic CPU time estimate of the order O (n-squared), where n is the number of nodes in the discretization of the boundary of the region being mapped. The method we present has an estimate of the order O(n), making it an approach of choice in many situations. The performance of the algorithm is illustrated by several numerical examples.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1987
Accession Number
ADA193903

Entities

People

  • S. T. O'donnell
  • Vladimir Rokhlin

Organizations

  • Yale University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Aspect Ratio
  • Boundaries
  • Cartography
  • Computations
  • Computer Science
  • Computers
  • Conformal Mapping
  • Differential Equations
  • Equations
  • Integral Equations
  • Linear Algebraic Equations
  • Linear Systems
  • Partial Differential Equations
  • Poisson Equation
  • Precision
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Graph Algorithms and Convex Optimization.