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High Order Whitney Forms on Simplices and the Question of Potentials Read chapter Read first chapter

2021 | OriginalPaper | Chapter

Applications of the PRESB Preconditioning Method for OPT-PDE Problems

Author : Owe Axelsson

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2019

Publisher: Springer International Publishing

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Abstract

Optimal control problems constrained by partial differential equations arise in a multitude of important applications. They lead mostly to the solution of very large scale algebraic systems to be solved, which must be done by iterative methods. The problems should then be formulated so that they can be solved fast and robust, which requires the construction of an efficient preconditioner. After reduction of a variable, a two-by-two block matrix system with square blocks arises for which such a preconditioner, PRESB is presented, involving the solution of two algebraic systems which are a linear combination of the matrix blocks. These systems can be solved by inner iterations, involving some available classical solvers to some relative, not very demanding tolerance.

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previous chapter Finite Difference Solutions of 2D Magnetohydrodynamic Channel Flow in a Rectangular Duct
next chapter Model Order Reduction Framework for Problems with Moving Discontinuities
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Metadata
Title
Applications of the PRESB Preconditioning Method for OPT-PDE Problems
Author
Owe Axelsson
Copyright Year
2021
Book
Numerical Mathematics and Advanced Applications ENUMATH 2019

Print ISBN: 978-3-030-55873-4

Electronic ISBN: 978-3-030-55874-1

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-55874-1_6

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