A Fast Algorithm for the Evaluation of Heat Potentials

Abstract

Numerical methods for solving the heat equation via potential theory have been hampered by the high cost of evaluating heat potentials. When M points are used in the discretization of the boundary and N time steps are computed, an amount of work of the order O(N-sq Msq) has traditionally been required. In this paper, we present an algorithm which requires an amount of work of the order O(NM), and we observe speedups of five orders of magnitude for large-scale problems. Thus, the method makes it possible to solve the heat equation by potential theory in practical situations.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1989
Accession Number
ADA211316

Entities

People

  • John Strain
  • Leslie Greengard

Organizations

  • Yale University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Coefficients
  • Computational Complexity
  • Computer Science
  • Computers
  • Crystal Growth
  • Equations
  • Errors
  • Fourier Series
  • Heat Energy
  • Integral Equations
  • Integrals
  • Interpolation
  • New York
  • Sequences
  • Universities

Fields of Study

  • Mathematics

Readers

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