An Iterative Method for Solving Electrostatic Problems

Abstract

The method of steepest descent is applied to the solution of electrostatic problems. The relationship between this method and the Rayleigh- Ritz, Galerkin's, and the method of least squares is outlined. Also, explicit error formulas are given for the rate of convergence for this method. It is shown that this method is also suitable for solving singular operator equations. In that case this method monotonically converges to the solution with minimum norm. Finally, it is shown that the technique yields as a by-product the smallest eigenvalue of the operator in the finite dimensional space in which the problem is solved. Numerical results are presented only for the electrostatic case to illustrate the validity of this procedure which show excellent agreement with other available data.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1981
Accession Number
ADA107740

Entities

People

  • Sadasiva M. Rao
  • Tapan K. Sarkar

Organizations

  • Rochester Institute of Technology

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Agreements
  • Convergence
  • Differential Equations
  • Eigenvalues
  • Electrical Engineering
  • Electromagnetic Fields
  • Electromagnetism
  • Electrostatic Fields
  • Engineering
  • Equations
  • Errors
  • Fourier Series
  • Geometry
  • Iterations
  • Method Of Moments
  • Military Research
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Operations Research
  • Plasma Physics.
  • Structural Dynamics.

Technology Areas

  • Space