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Title: Multigrid methods in convex optimization with application to structural design
Author: Mohammed, Sudaba Aref
ISNI:       0000 0004 5370 9646
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2016
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This dissertation has investigated the use of multigrid methods in certain classes of optimization problems, with emphasis on structural, namely topology optimization. We have investigated the solution bound constrained optimization problems arising in discretization by the finite element method, such as elliptic variational inequalities. For these problems we have proposed a "direct" multi grid approach which is a generalization of existing multigrid methods for variational inequalities. We have proposed a nonlinear first order method as a smoother that reduces memory requirements and improves the efficiency of the resulting algorithm compared to the second order method (Newton's methods), as documented on several numerical examples. The project further investigates the use of multigrid techniques in topology optimization. Topology optimization is a very practical and efficient tool for the design of lightweight structures and has many applications, among others in automotive and aircraft industry. The project studies the employment of multigrid methods in the solution of very large linear systems with sparse symmetric positive definite matrices arising in interior point methods where, traditionally, direct techniques are used. The proposed multigrid approach proves to be more efficient than that with the direct solvers. In particular, it exhibits linear dependency of the computational effort on the problem size.
Supervisor: Not available Sponsor: Ministry of Higher Education and Scientific Research ; Republic of Iraq
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics