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Nonlinear control for non-Newtonian flows

Alrashidi, Azizah (2015)
Ph.D. thesis, University of Birmingham.

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Abstract

PDE-constrained optimization is an important area in the field of numerical analysis, with problems arising in a wide variety of applications including optimal design, optimal control and parameter estimation. The aim of such problems is to minimize a functional J(u,d) whilst adhering to constraints posed by a system of partial differential equations (PDE), with u and d used respectively to denote the state and control of the system.

In this thesis, we describe the steady-state generalized Stokes equations for incompressible fluids. We proceed to derive the weak formulation of the problem, and show that the resulting system may be written in terms of a mixed formulation of the Stokes problem. Based on this formulation, the problem is discretized through use of the Galerkin finite element method, before investigating control problems based on the generalized Stokes equations, along with numerical experimentation.

This work will be used to achieve the main aim of this thesis, namely the exploration and investigation of solution methods for optimal control problems constrained by non- Newtonian flow. Ultimately, an iterative solution method designed for such problems coupled with an appropriate preconditioning strategy will be described and analyzed, and used to produce effective numerical results.

Type of Work:Ph.D. thesis.
Supervisor(s):Loghin, Daniel
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Subjects:QA Mathematics
Institution:University of Birmingham
ID Code:5777
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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