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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr


IMPACT FACTOR 2017: 0.658

CiteScore 2017: 1.05

SCImago Journal Rank (SJR) 2017: 1.291
Source Normalized Impact per Paper (SNIP) 2017: 0.893

Mathematical Citation Quotient (MCQ) 2017: 0.76

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1609-9389
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Volume 16, Issue 3

Issues

Computational Comparison of Surface Metrics for PDE Constrained Shape Optimization

Volker Schulz / Martin Siebenborn
Published Online: 2016-02-26 | DOI: https://doi.org/10.1515/cmam-2016-0009

Abstract

We compare surface metrics for shape optimization problems with constraints, consisting mainly of partial differential equations (PDE), from a computational point of view. In particular, classical Laplace–Beltrami type metrics are compared with Steklov–Poincaré type metrics. The test problem is the minimization of energy dissipation of a body in a Stokes flow. We therefore set up a quasi-Newton method on appropriate shape manifolds together with an augmented Lagrangian framework, in order to enable a straightforward integration of geometric constraints for the shape. The comparison is focussed towards convergence behavior as well as effects on the mesh quality during shape optimization.

Keywords: PDE constrained shape optimization; optimization on Riemannian manifolds; Stokes problem

MSC 2010: 49Q10; 65K10; 65N30

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About the article

Received: 2015-12-10

Revised: 2016-02-05

Accepted: 2016-02-10

Published Online: 2016-02-26

Published in Print: 2016-07-01


Funding Source: Deutsche Forschungsgemeinschaft

Award identifier / Grant number: Schu804/12-1

This work has been partly supported by the Deutsche Forschungsgemeinschaft within the Priority program SPP 1648 “Software for Exascale Computing” under contract number Schu804/12-1. Furthermore, we acknowledge support by the Sino-German Science Center (grant id 1228) on the occasion of the Chinese-German Workshop on Computational and Applied Mathematics in Augsburg 2015.


Citation Information: Computational Methods in Applied Mathematics, Volume 16, Issue 3, Pages 485–496, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2016-0009.

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