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