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Block triangular preconditioning for time‐dependent Stokes control
Author(s) -
Pearson John W.
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510349
Subject(s) - preconditioner , saddle point , tridiagonal matrix , solver , block (permutation group theory) , diagonal , triangular matrix , block matrix , saddle , matrix (chemical analysis) , band matrix , mathematics , mathematical optimization , optimization problem , computer science , iterative method , eigenvalues and eigenvectors , physics , symmetric matrix , combinatorics , geometry , pure mathematics , square matrix , quantum mechanics , invertible matrix , materials science , composite material
We consider the numerical solution of time‐dependent Stokes control problems, an important class of flow control problems within the field of PDE‐constrained optimization. The problems we examine lead to large and sparse matrix systems which, with suitable rearrangement, can be written in block tridiagonal form, with the diagonal blocks given by saddle point systems. Using previous results for preconditioning PDE‐constrained optimization and fluid dynamics problems, along with well‐studied saddle point theory, we construct a block triangular preconditioner for the matrix systems. Numerical experiments verify the effectiveness of our solver. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)