A New Preconditioning Strategy for Solving a Class of Time-Dependent PDE-Constrained Optimization Problems
Year: 2014
Journal of Computational Mathematics, Vol. 32 (2014), Iss. 3 : pp. 215–232
Abstract
In this paper, by exploiting the special block and sparse structure of the coefficient matrix, we present a new preconditioning strategy for solving large sparse linear systems arising in the time-dependent distributed control problem involving the heat equation with two different functions. First a natural order-reduction is performed, and then the reduced-order linear system of equations is solved by the preconditioned MINRES algorithm with a new preconditioning techniques. The spectral properties of the preconditioned matrix are analyzed. Numerical results demonstrate that the preconditioning strategy for solving the large sparse systems discretized from the time-dependent problems is more effective for a wide range of mesh sizes and the value of the regularization parameter.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1401-CR3
Journal of Computational Mathematics, Vol. 32 (2014), Iss. 3 : pp. 215–232
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: PDE-constrained optimization Reduced linear system of equations Preconditioning Saddle point problem Krylov subspace methods.