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Efficient solution of parabolic equations by Krylov approximation methodsNumerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.
Document ID
19930004221
Document Type
Contractor Report (CR)
Authors
Gallopoulos, E. (Illinois Univ. Urbana-Champaign., United States)
Saad, Y. (Minnesota Univ. Minneapolis., United States)
Date Acquired
September 6, 2013
Publication Date
March 1, 1990
Subject Category
NUMERICAL ANALYSIS
Report/Patent Number
RIACS-TR-90-14
NASA-CR-191235
NAS 1.26:191235
Funding Number(s)
CONTRACT_GRANT: NCC2-387
CONTRACT_GRANT: NSF CCR-87-17942
CONTRACT_GRANT: DE-FG02-85ER-25001
CONTRACT_GRANT: AF-AFOSR-0044-90
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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