Preconditioned polynomial iterative acceleration methods for block tridiagonal systems
Preconditionings based on incomplete block odd-even cyclic reduction for Chebyshev and Conjugate Gradient polynomial iterative methods have been shown to be very effective for accelerating the convergence of the solution of linear systems which arise from discrete approximations of elliptic partial differential equations. The main contribution of this paper is to extend these methods to the important case of Red/Black partitioning of equations and unknowns and to demonstrate that a significant reduction in computations can be realized by applying preconditioned polynomial methods to the ''reduced systems,'' which are obtained from the original systems by eliminating approximately half of the unknowns. This paper also compares the performance of several preconditioned polynomial methods for solving the two-dimensional diffusion equation on the CYBER 205 vector computer. The most effective methods tested are shown to be (1) the classical reduced system conjugate gradient method with preconditioner D/sub B/, the tridiagonal matrix associated with the black unknowns, and (2) the new reduced system conjugate gradient method with preconditioner based on incomplete block odd-even cyclic reduction. Of these methods, the latter is to be preferred for slow converging problems. 22 refs., 1 fig., 7 tabs.
- Research Organization:
- Bettis Atomic Power Lab., West Mifflin, PA (USA)
- DOE Contract Number:
- AC11-76PN00014
- OSTI ID:
- 7181980
- Report Number(s):
- WAPD-T-2885; CONF-861186-1; ON: DE87000901
- Country of Publication:
- United States
- Language:
- English
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