A Conjugate Gradient Approach to Nonlinear Elliptic Boundary Value Problems in Irregular Regions,

Abstract

A version of the conjugate gradient method is proposed for solving discrete approximations to nonlinear elliptic boundary value problems over irregular regions. The convergence rate is usually independent of the discretization, but each step requires the solution of a Poisson equation on the region; thus a fast Poisson solver yields a fast method for the general problem. Details are given for the standard 5-point approximation to the differential equation, with the Poisson equations being solved by the Buneman algorithm after some preprocessing; numerical examples are given. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1973
Accession Number
AD0758693

Entities

People

  • James W. Daniel
  • Richard Bartels

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Convergence
  • Differential Equations
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Poisson Equation

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)