Marching Algorithms for Elliptic Boundary Value Problems II: The Non-Constant Coefficient Case.
Technical rept. Sep 74-May 75,
HARVARD UNIV CAMBRIDGE MASS AIKEN COMPUTATION LAB
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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 On sup 2 and 0n sup 2 log nk 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 DYakanov-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.
- Theoretical Mathematics