Marching Algorithms for Elliptic Boundary Value Problems II: The Non-Constant Coefficient Case.

Abstract

The marching and generalized marching algorithms of Part I are extended to non-constant coefficient problems in which the elliptic operator is separable, once a suitable set of polynomials, which play a role analogous to the Chebyshev polynomials in the constant coefficient case, has been determined. These methods require O(n sup 2) and 0(n sup 2 log n/k) operations, respectively, to solve a problem on an n x n grid, and have numerical stability characteristics similar to their constant coefficient counterparts. Problems in which the elliptic operator is not separable are treated using a D'Yakanov-Gunn iteration in which a sequence of separable problems is solved. The rate of convergence of this iteration is shown to be essentially independent of n.

Document Details

Document Type
Technical Report
Publication Date
May 28, 1975
Accession Number
ADA011106

Entities

People

  • Randolph E. Bank

Organizations

  • Harvard University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Chebyshev Polynomials
  • Coefficients
  • Convergence
  • Iterations
  • Mathematics
  • Polynomials
  • Sequences

Fields of Study

  • Mathematics

Readers

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