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Approximate shape gradients for interface problems

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posted on 11.06.2020, 09:11 by A Paganini

Shape gradients of shape differentiable shape functionals constrained to an interface problem (IP) can be formulated in two equivalent ways. Both formulations rely on the solution of two IPs, and their equivalence breaks down when these IPs are solved approximatively. We establish which expression for the shape gradient offers better accuracy for approximations by means of finite elements. Great effort is devoted to provide numerical evidence of the theoretical considerations.


Funding

The work of A. Paganini was partly supported by ETH Grant CH1-02 11-1.

History

Citation

Paganini A. (2015) Approximate Shape Gradients for Interface Problems. In: Pratelli A., Leugering G. (eds) New Trends in Shape Optimization. International Series of Numerical Mathematics, vol 166. Birkhäuser, Cham

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

AM (Accepted Manuscript)

Published in

New Trends in Shape Optimization. International Series of Numerical Mathematics

Volume

166

Publisher

Birkhäuser, Cham

isbn

978-3-319-17563-8

Copyright date

2015

Editors

Pratelli A., Leugering G.

Book series

International Series of Numerical Mathematics

Language

en

Publisher version

https://link.springer.com/chapter/10.1007/978-3-319-17563-8_9