University of Jyväskylä

Dissertation: Shape optimization utilizing consistent sensitivities (Toivanen)

Start date: Aug 26, 2010 12:00 PM

End date: Aug 26, 2010 03:00 PM

Location: Mattilanniemi, Agora, Auditorio 2

M.Sc. Jukka Toivanen defends his doctoral dissertation titled ”Shape optimization utilizing consistent sensitivities”. Opponent Docent, Dr. Ing. Eduard Rohan (University of West Bohemia, Czech Republic) and custos Professor Raino A.E. Mäkinen (University of Jyväskylä).


This thesis deals with gradient based methods to solve shape optimization problems governed by partial differential equations (PDE). Automatic differentiation (AD) techniques provide a straightforward way to augment new and existing PDE solvers with derivative computation routines. We present a novel implementation of the so called sparse forward mode AD, which provides an automatic way to exploit sparsity in derivative computations. Using this technique it is possible to compute large sparse Jacobians of vector functions so that only minimal changes to the original code are required. Moreover, this technique can be used in the context of the discrete adjoint approach to efficiently compute large shape gradients. The implementation has only slightly larger computational overhead than traditional dense mode implementations.

The AD technique is used to implement shape sensitivity analysis capabilities into an existing electromagnetic solver based on the methods of moments, and the solver is used to solve various shape optimization problems related to antenna design. Sensitivity analysis is also implemented in the context of the finite element method, and this implementation is used for example to solve a fibre orientation control problem in a simplified paper machine headbox. Shape optimization governed by the Bernoulli free boundary problem is also considered.

To this end, a so called pseudo solid approach is used to develop a solver that enables efficient solution of the free boundary problem, as well as the shape sensitivity analysis.

Keywords: shape optimization, sensitivity analysis, automatic differentiation

Further information:

Jukka Toivanen, tel. 050 304 1579,

The dissertation is published in the series Jyväskylä Studies in Computing as number 116. ISSN 1456-5390, ISBN 978-951-39-3968-7. Inquiries: tel. (014) 260 3487,

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