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International Journal of Computer Mathematics Volume 85, 2008 - Issue 10: INNOVATIVE ALGORITHMS IN SCIENCE AND ENGINEERING
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Original Articles

Level set method with topological derivatives in shape optimization

Piotr Fulmanski Faculty of Mathematics, University of Łódź, Łódź, Poland
,
Antoine Laurain Institut Elie Cartan UMR 7502, Nancy-Université, CNRS, INRIA, Vandoeuvre-les-Nancy Cedex, France
,
Jean-François Scheid Institut Elie Cartan UMR 7502, Nancy-Université, CNRS, INRIA, Vandoeuvre-les-Nancy Cedex, France
&
Jan Sokołowski Institut Elie Cartan UMR 7502, Nancy-Université, CNRS, INRIA, Vandoeuvre-les-Nancy Cedex, FranceCorrespondence[email protected]
Pages 1491-1514 | Received 22 Aug 2006, Accepted 19 Nov 2007, Published online: 01 Sep 2008

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Samuel Amstutz. (2011) Analysis of a level set method for topology optimization. Optimization Methods and Software 26:4-5, pages 555-573.
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Shengfeng Zhu, Xiaoxia Dai & Chunxiao Liu. (2011) A variational binary level-set method for elliptic shape optimization problems. International Journal of Computer Mathematics 88:14, pages 3026-3045.
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Wenjing Yan, Yingyuan Li & Jiangyong Hou. (2022) Shape optimization for an obstacle located in incompressible Boussinesq flow. Computers & Fluids 240, pages 105431.
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F. Le Louër & M.-L. Rapún. (2022) Topological Imaging Methods for the Iterative Detection of Multiple Impedance Obstacles. Journal of Mathematical Imaging and Vision 64:3, pages 321-340.
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Wenjing Yan, Feifei Jing, Jiangyong Hou, Zhiming Gao & Nannan Zheng. (2020) An Iterative Method for Shape Optimal Design of Stokes–Brinkman Equations with Heat Transfer Model. Mathematical Problems in Engineering 2020, pages 1-11.
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Kandula Eswara Sai Kumar & Sourav Rakshit. 2020. Advances in Mechanical Engineering. Advances in Mechanical Engineering 1511 1520 .
Antoine Laurain. (2018) A level set-based structural optimization code using FEniCS. Structural and Multidisciplinary Optimization 58:3, pages 1311-1334.
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Antoine Laurain. (2017) Stability Analysis of the Reconstruction Step of the Voronoi Implicit Interface Method. SIAM Journal on Numerical Analysis 55:1, pages 1-30.
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Antoine Laurain & Houcine Meftahi. (2016) Shape and parameter reconstruction for the Robin transmission inverse problem. Journal of Inverse and Ill-posed Problems 24:6, pages 643-662.
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A. Myśliński. (2015) Piecewise constant level set method for topology optimization of unilateral contact problems. Advances in Engineering Software 80, pages 25-32.
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Li Tian, Dai Xiaoxia & Zhang Chengwei. (2015) Two Algorithms for a Class of Elliptic Problems in Shape Optimization. Mathematical Problems in Engineering 2015, pages 1-8.
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V Melicher & V Vrábel’. (2013) On a continuation approach in Tikhonov regularization and its application in piecewise-constant parameter identification. Inverse Problems 29:11, pages 115008.
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N. P. van Dijk, K. Maute, M. Langelaar & F. van Keulen. (2013) Level-set methods for structural topology optimization: a review. Structural and Multidisciplinary Optimization 48:3, pages 437-472.
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Andrzej Myśliński. 2013. System Modeling and Optimization. System Modeling and Optimization 407 416 .
Shengfeng Zhu, Qingbiao Wu & Chunxiao Liu. (2011) Shape and topology optimization for elliptic boundary value problems using a piecewise constant level set method. Applied Numerical Mathematics 61:6, pages 752-767.
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Shengfeng Zhu, Chunxiao Liu & Qingbiao Wu. (2010) Binary level set methods for topology and shape optimization of a two-density inhomogeneous drum. Computer Methods in Applied Mechanics and Engineering 199:45-48, pages 2970-2986.
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Shengfeng Zhu, Qingbiao Wu & Chunxiao Liu. (2010) Variational piecewise constant level set methods for shape optimization of a two-density drum. Journal of Computational Physics 229:13, pages 5062-5089.
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G. Cardone, S. A. Nazarov & J. Sokolowski. (2010) Asymptotic Analysis, Polarization Matrices, and Topological Derivatives for Piezoelectric Materials with Small Voids. SIAM Journal on Control and Optimization 48:6, pages 3925-3961.
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S. M. Giusti, A. A. Novotny & J. Sokołowski. (2009) Topological derivative for steady-state orthotropic heat diffusion problem. Structural and Multidisciplinary Optimization 40:1-6, pages 53-64.
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Jan Sokołowski & Antoni Żochowski. 2010. Computer Methods in Mechanics. Computer Methods in Mechanics 75 98 .
Arnaud Münch. (2009) Optimal Internal Dissipation of a Damped Wave Equation Using a Topological Approach. International Journal of Applied Mathematics and Computer Science 19:1, pages 15-38.
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Jan Sokolowski & Antoni Zochowski. 2009. Encyclopedia of Optimization. Encyclopedia of Optimization 3908 3918 .

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