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Fast iterative solvers for large matrix systems arising from time-dependent Stokes control problems. (English) Zbl 1346.65035

Summary: In this manuscript we consider the development of fast iterative solvers for Stokes control problems, an important class of partial differential equation-constrained optimization problems. In particular we wish to develop effective preconditioners for the matrix systems arising from finite element discretizations of time-dependent variants of such problems. To do this we consider a suitable rearrangement of the matrix systems, and exploit the saddle point structure of many of the relevant sub-matrices involved – we may then use this to construct representations of these sub-matrices based on good approximations of their \((1, 1)\)-block and Schur complement. We test our recommended iterative methods on a distributed control problem with Dirichlet boundary conditions, and on a time-periodic problem.

MSC:

65K10 Numerical optimization and variational techniques
49J20 Existence theories for optimal control problems involving partial differential equations
65F05 Direct numerical methods for linear systems and matrix inversion

Software:

HSL_MI20; IFISS; AGMG
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Full Text: DOI Link

References:

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