Open Access
Issue |
ESAIM: M2AN
Volume 59, Number 3, May-June 2025
|
|
---|---|---|
Page(s) | 1505 - 1529 | |
DOI | https://doi.org/10.1051/m2an/2025033 | |
Published online | 04 June 2025 |
- G. Allaire, C. Dapogny and F. Jouve, Shape and topology optimization, in Differential Geometric Partial Differential Equations: Part II. Vol. 22 of Handbook of Numerical Analysis. Elsevier, Amsterdam, Netherlands (2021) 3–124. [Google Scholar]
- S. Bartels and M. Milicevic, Efficient iterative solution of finite element discretized nonsmooth minimization problems. Comput. Math. Appl. 80 (2020) 588–603. [CrossRef] [MathSciNet] [Google Scholar]
- S. Bartels and G. Wachsmuth, Numerical approximation of optimal convex shapes. SIAM J. Sci. Comput. 42 (2020) A1226–A1244. [CrossRef] [Google Scholar]
- P. Bastian, M. Blatt, A. Dedner, N.-A. Dreier, C. Engwer, R. Fritze, C. Gr¨aser, C. Grũninger, D. Kempf, R. Klöfkorn, M. Ohlberger and O. Sander, The Dune framework: basic concepts and recent developments. Comput. Math. App. 81 (2021) 75–112. [Google Scholar]
- D. Bucur and J.P. Zolesio, N-dimensional shape optimization under capacitary constraint. J. Differ. Equ. 123 (1995) 504–522. [CrossRef] [Google Scholar]
- D. Chenais and E. Zuazua, Finite-element approximation of 2d elliptic optimal design. J. Math. Pures App. 85 (2006) 225–249. [CrossRef] [Google Scholar]
- K. Deckelnick, P.J. Herbert and M. Hinze, A novel W1,∞ approach to shape optimisation with Lipschitz domains. ESAIM: COCV 28 (2022) 2. [CrossRef] [EDP Sciences] [Google Scholar]
- K. Deckelnick, P.J. Herbert and M. Hinze, PDE constrained shape optimisation with first-order and Newton-type methods in the W1,∞ topology. Optim. Methods Softw. (2024). DOI: 10.1080/10556788.2024.2424525. [Google Scholar]
- A. Dedner and M. Nolte, The Dune Python module. Preprint arXiv:1807.05252 (2018). [Google Scholar]
- A. Dedner, M. Nolte and R. Klöfkorn, Python bindings for the DUNE-FEM module (2020). https://zenodo.org/records/3706994. [Google Scholar]
- M.C. Delfour and J.-P. Zolésio, Shapes and Geometries: Analysis, Differential Calculus, and Optimization. Society for Industrial and Applied Mathematics, USA (2001). [Google Scholar]
- M.C. Delfour and J.P. Zolesio, Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization, 2nd edition. Advances in Design and Control. Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) (2011). [Google Scholar]
- K. Eppler, H. Harbrecht and R. Schneider, On convergence in elliptic shape optimization. SIAM J. Control Optim. 46 (2007) 61–83. [CrossRef] [MathSciNet] [Google Scholar]
- I. Fumagalli, N. Parolini and M. Verani, Shape optimization for Stokes flows: a finite element convergence analysis. ESAIM: Math. Model. Numer. Anal. 49 (2015) 921–951. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- W. Gong and S. Zhu, On discrete shape gradients of boundary type for PDE-constrained shape optimization. SIAM J. Numer. Anal. 59 (2021) 1510–1541. [CrossRef] [MathSciNet] [Google Scholar]
- J. Heinonen, T. Kipelainen and O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations. Courier Dover Publications (2018). [Google Scholar]
- A. Henrot and M. Pierre, Shape Variation and Optimization: A Geometrical Analysis. EMS Tracts in Mathematics. European Mathematical Society (2018). [CrossRef] [Google Scholar]
- P.J. Herbert, J.A. Pinzon Escobar and M. Siebenborn, Shape optimization in W1,∞ with geometric constraints: a study in distributed-memory systems. Preprint arXiv:2309.15607 (2023). [Google Scholar]
- M. Hinze, R. Pinnau, M. Ulbrich and S. Ulbrich, Optimization with PDE Constraints. Vol. 23. Springer Science & Business Media (2008). [Google Scholar]
- R. Hiptmair, A. Paganini and S. Sargheini, Comparison of approximate shape gradients. BIT Numer. Math. 55 (2015) 459–485. [CrossRef] [Google Scholar]
- J.A. Iglesias, K. Sturm and F. Wechsung, Two-dimensional shape optimization with nearly conformal transformations. SIAM J. Sci. Comput. 40 (2018) A3807–A3830. [CrossRef] [Google Scholar]
- B. Kiniger and B. Vexler, A priori error estimates for finite element discretizations of a shape optimization problem. ESAIM: Math. Model. Numer. Anal. 47 (2013) 1733–1763. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- P.M. Müller, CAD-free adjoint shape optimization of floating vessels. Ph.D. thesis, Hamburg University of Technology (2024). [Google Scholar]
- P.M. Müller, N. Kühl, M. Siebenborn, K. Deckelnick, M. Hinze and T. Rung, A novel p-harmonic descent approach applied to fluid dynamic shape optimization. Struct. Multidiscipl. Optim. 64 (2021) 3489–3503. [CrossRef] [Google Scholar]
- N. Schlömer, pygmsh: A Python frontend for Gmsh (January 2022). https://zenodo.org/records/5913837. [Google Scholar]
- J. Soko lowski and J.P. Zolésio, Introduction to Shape Optimization: Shape Sensitivity Analysis. Lecture Notes in Computer Science. Springer-Verlag (1992). [Google Scholar]
- S. Zhu and Z. Gao, Convergence analysis of mixed finite element approximations to shape gradients in the Stokes equation. Comput. Methods Appl. Mech. Eng. 343 (2019) 127–150. [CrossRef] [Google Scholar]
- S. Zhu, X. Hu and Q. Liao, Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization. BIT Numer. Math. 60 (2020) 853–878. [CrossRef] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.