A Direct Method for the Discrete Solution of Separable Elliptic Equations

A Direct Method for the Discrete Solution of Separable Elliptic Equations

This paper extends the direct method of cyclic reduction to linear systems which result from the discretization of separable elliptic equations with Dirichlet, Neumann, or periodic boundary conditions. For an m × n net, the operation count is proportional to mn log2 n and mn storage locations are re...

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Veröffentlicht in:SIAM journal on numerical analysis 1974-12, Vol.11 (6), p.1136-1150
1. Verfasser: Swarztrauber, Paul N.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Boundary conditions
Elliptic equations
Factorization
Fourier transforms
Linear systems
Matrices
Methods
Partial differential equations
Poisson equation
Polynomials
Preprocessing
Scalars
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Zusammenfassung:This paper extends the direct method of cyclic reduction to linear systems which result from the discretization of separable elliptic equations with Dirichlet, Neumann, or periodic boundary conditions. For an m × n net, the operation count is proportional to mn log2 n and mn storage locations are required.
ISSN:0036-1429
1095-7170
DOI:10.1137/0711086