Strang's Circulant Preconditioners for Differential-Algebric Equations
by
Siu-Long Lei
University of Macau
Coauthors: Xiao-Qing Jin (University of Macau)

We consider linear constant coefficient differential-algebric equations (DAEs) Ax'(t)+Bx(t)=f(t) where A, B are m-by-m matrices and A is singular. If the matrix pencil \lambdaA+B is regular, the system of DAEs is solvable and can be seperated to two uncoupled subsystems. one of them can be solved anatically and the other one is a system of ordinary differential equations (ODEs). We discretize the ODEs by the boundary value methods (BVMs) and solve the linear system by using Krylov subspace methods with Strang's block-circulant preconditioners. It was shown that the preconditioners are nonsingular when the BVM is stable and the eigenvalues of preconditioned matrices are clustered. Then the number of iterations of solving the preconditioned systems by Krylov subspace methods (for instant, the GMRES method and BICGSTAB method) is bounded by a constant that is independent of the discretization mesh. Numerical results are also given.

Date received: January 30, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeb-35.