Convergence-Theoretics of Classical and Krylov Waveform Relaxation Methods for Differential=Algebraic Equations

Yao-Lin JIANG  Wai-Shing LUK  Omar WING  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A   No.10   pp.1961-1972
Publication Date: 1997/10/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on VLSI Design and CAD Algorithms)
Category: 
Keyword: 
waveform relaxation methods,  Krylov subspace methods,  differential-algebraic equations,  circuit simulation,  

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Summary: 
We present theoretical results on the convergence of iterative methods for the solution of linear differential-algebraic equations arising form circuit simulation. The iterative methods considered include the continuous-time and discretetime waveform relaxation methods and the Krylov subspace methods in function space. The waveform generalized minimal residual method for solving linear differential-algebraic equations in function space is developed, which is one of the waveform Krylov subspace methods. Some new criteria for convergence of these iterative methods are derived. Examples are given to verify the convergence conditions.