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The test problem is the minimization of energy dissipation of a body in a Stokes flow.\nWe 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\neffects on the mesh quality during shape optimization.<\/jats:p>","DOI":"10.1515\/cmam-2016-0009","type":"journal-article","created":{"date-parts":[[2016,2,26]],"date-time":"2016-02-26T18:38:56Z","timestamp":1456511936000},"page":"485-496","source":"Crossref","is-referenced-by-count":65,"title":["Computational Comparison of Surface Metrics for PDE Constrained Shape Optimization"],"prefix":"10.1515","volume":"16","author":[{"given":"Volker","family":"Schulz","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Trier, 54286 Trier, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Siebenborn","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Trier, 54286 Trier, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2016,2,26]]},"reference":[{"key":"2023033112444845766_j_cmam-2016-0009_ref_001_w2aab3b7d658b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"Absil P., Mahony R. and Sepulchre R.,\nOptimization Algorithms on Matrix Manifolds,\nPrinceton University Press, Princeton, 2008.","DOI":"10.1515\/9781400830244"},{"key":"2023033112444845766_j_cmam-2016-0009_ref_002_w2aab3b7d658b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"Borz\u00ec A. and Schulz V.,\nComputational Optimization of Systems Governed by Partial Differential Equations,\nSIAM Book Ser. Comput. Sci. Eng. 8,\nSIAM, Philadelphia, 2012.","DOI":"10.1137\/1.9781611972054"},{"key":"2023033112444845766_j_cmam-2016-0009_ref_003_w2aab3b7d658b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"Conn A. R., Gould N. I. M. and Toint P. L.,\nLancelot,\nSpringer, Berlin, 1992.","DOI":"10.1007\/978-3-662-12211-2"},{"key":"2023033112444845766_j_cmam-2016-0009_ref_004_w2aab3b7d658b1b6b1ab2ab4Aa","unstructured":"Delfour M. C. and Zol\u00e9sio J.-P.,\nShapes and Geometries: Analysis, Differential Calculus, and Optimization,\nAdv. Des. Control,\nSIAM, Philadelphia, 2001."},{"key":"2023033112444845766_j_cmam-2016-0009_ref_005_w2aab3b7d658b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"Eppler K., Harbrecht H. and Schneider R.,\nOn convergence in elliptic shape optimization,\nSIAM J. Control Optim. 46 (2007), no. 1, 61\u201383.","DOI":"10.1137\/05062679X"},{"key":"2023033112444845766_j_cmam-2016-0009_ref_006_w2aab3b7d658b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"Gangl P., Laurain A., Meftahi H. and Sturm K.,\nShape optimization of an electric motor subject to nonlinear magnetostatics,\npreprint 2015, http:\/\/arxiv.org\/abs\/1501.04752.","DOI":"10.1137\/15100477X"},{"key":"2023033112444845766_j_cmam-2016-0009_ref_007_w2aab3b7d658b1b6b1ab2ab7Aa","unstructured":"Haack W.,\nGescho\u00dfformen kleinsten Wellenwiderstandes,\nBericht der Lilienthal-Gesellschaft 136 (1941), no. 1, 14\u201328."},{"key":"2023033112444845766_j_cmam-2016-0009_ref_008_w2aab3b7d658b1b6b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"Michor P. and Mumford D.,\nRiemannian geometries on spaces of plane curves,\nJ. Eur. Math. Soc. (JEMS) 8 (2006), 1\u201348.","DOI":"10.4171\/JEMS\/37"},{"key":"2023033112444845766_j_cmam-2016-0009_ref_009_w2aab3b7d658b1b6b1ab2ab9Aa","unstructured":"Mohammadi B. and Pironneau O.,\nApplied Shape Optimization for Fluids,\nNum. Math. Sci. Comput.,\nClarendon Press, Oxford, 2001."},{"key":"2023033112444845766_j_cmam-2016-0009_ref_010_w2aab3b7d658b1b6b1ab2ac10Aa","doi-asserted-by":"crossref","unstructured":"N\u00e4gel A., Schulz V., Siebenborn M. and Wittum G.,\nScalable shape optimization methods for structured inverse modeling in 3D diffusive processes,\nComput. Vis. Sci. 17 (2015), 79\u201388.","DOI":"10.1007\/s00791-015-0248-9"},{"key":"2023033112444845766_j_cmam-2016-0009_ref_011_w2aab3b7d658b1b6b1ab2ac11Aa","unstructured":"Paganini A.,\nApproximative shape gradients for interface problems,\ntechnical report 2014-12, Seminar for Applied Mathematics, ETH Z\u00fcrich, 2014."},{"key":"2023033112444845766_j_cmam-2016-0009_ref_012_w2aab3b7d658b1b6b1ab2ac12Aa","doi-asserted-by":"crossref","unstructured":"Pironneau O.,\nOn optimum profiles in stokes flow,\nJ. Fluid Mech. 59 (1973), no. 1, 117\u2013128.","DOI":"10.1017\/S002211207300145X"},{"key":"2023033112444845766_j_cmam-2016-0009_ref_013_w2aab3b7d658b1b6b1ab2ac13Aa","doi-asserted-by":"crossref","unstructured":"Ring W. and Wirth B.,\nOptimization methods on Riemannian manifolds and their application to shape space,\nSIAM J. Optim. 22 (2012), 596\u2013627.","DOI":"10.1137\/11082885X"},{"key":"2023033112444845766_j_cmam-2016-0009_ref_014_w2aab3b7d658b1b6b1ab2ac14Aa","doi-asserted-by":"crossref","unstructured":"Schmidt S., Ilic C., Schulz V. and Gauger N.,\nThree dimensional large scale aerodynamic shape optimization based on the shape calculus,\nAIAA J. 51 (2013), no. 11, 2615\u20132627.","DOI":"10.2514\/1.J052245"},{"key":"2023033112444845766_j_cmam-2016-0009_ref_015_w2aab3b7d658b1b6b1ab2ac15Aa","doi-asserted-by":"crossref","unstructured":"Schulz V.,\nA Riemannian view on shape optimization,\nFound. Comput. 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