Open Access
Issue
ESAIM: M2AN
Volume 54, Number 1, January-February 2020
Page(s) 181 - 228
DOI https://doi.org/10.1051/m2an/2019056
Published online 27 January 2020
  1. G. Allaire, In: Vol. of 58 Conception optimale de structures, Springer (2007). [Google Scholar]
  2. G. Allaire, F. Jouve and A.-M. Toader, Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194 (2004) 363–393. [Google Scholar]
  3. G. Allaire, F. De Gournay, F. Jouve and A.-M. Toader, Structural optimization using topological and shape sensitivity via a level set method. Control Cybern. 34 (2005) 59. [Google Scholar]
  4. G. Allaire, C. Dapogny and P. Frey, Shape optimization with a level set based mesh evolution method. Comput. Methods Appl. Mech. Eng. 282 (2014) 22–53. [Google Scholar]
  5. G. Allaire, C. Dapogny, G. Delgado and G. Michailidis, Multi-phase structural optimization via a level set method. ESAIM: COCV 20 (2014) 576–611. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  6. G. Allaire, F. Jouve and G. Michailidis, Molding direction constraints in structural optimization via a level-set method. In: Variational Analysis and Aerospace Engineering. Springer (2016) 1–39. [Google Scholar]
  7. G. Allaire, F. Jouve and G. Michailidis, Thickness control in structural optimization via a level set method. Struct. Multi. Optim. 53 (2016) 1349–1382. [CrossRef] [Google Scholar]
  8. L. Ambrosio, Geometric evolution problems, distance function and viscosity solutions. In: Calculus of Variations and Partial Differential Equations. Springer (2000) 5–93. [Google Scholar]
  9. N. Amenta, S. Choi and R.K. Kolluri, The power crust, unions of balls, and the medial axis transform. Comput. Geom. 19 (2001) 127–153. [Google Scholar]
  10. D. Attali, J.-D. Boissonnat and H. Edelsbrunner, Stability and computation of medial axes-a state-of-the-art report. In: Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration. Springer (2009) 109–125. [CrossRef] [Google Scholar]
  11. P. Azérad, Equations de Navier-Stokes en bassin peu profond. Ph.D. thesis, Université de Neuchâtel (1995). [Google Scholar]
  12. P. Azérad and J. Pousin, Inégalité de poincaré courbe pour le traitement variationnel de l’équation de transport. C.R. Acad. Sci. Ser. 1: Math. 322 (1996) 721–727. [Google Scholar]
  13. A. Bensalah, Une approche nouvelle de la modélisation mathématique et numérique en aéroacoustique par les équations de Goldstein et applications en aéronautique, Ph.D. thesis, Université Paris Saclay (2018). [Google Scholar]
  14. G. Bellettini, Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations, In Vol. 12. Springer (2014). [Google Scholar]
  15. P. Cannarsa and P. Cardaliaguet, Representation of equilibrium solutions to the table problem of growing sandpiles. J. Eur. Math. Soc. 6 (2004) 435–464. [CrossRef] [Google Scholar]
  16. S. Chen, M.Y. Wang and A.Q. Liu, Shape feature control in structural topology optimization. Comput.-Aided Des. 40 (2008) 951–962. [CrossRef] [Google Scholar]
  17. G. Cheng, Y. Mei and X. Wang, A feature-based structural topology optimization method. In: IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials. Springer (2006) 505–514. [Google Scholar]
  18. C. Chicone, Ordinary Differential Equations with Applications. Springer, New York (1999). [Google Scholar]
  19. D.L. Chopp, Another look at velocity extensions in the level set method. SIAM J. Sci. Comput. 31 (2009) 3255–3273. [Google Scholar]
  20. C. Dapogny and P. Frey, Computation of the signed distance function to a discrete contour on adapted triangulation. Calcolo 49 (2012) 193–219. [CrossRef] [Google Scholar]
  21. C. Dapogny, C. Dobrzynski and P. Frey, Three-dimensional adaptive domain remeshing, implicit domain meshing, and applications to free and moving boundary problems. J. Comput. Phys. 262 (2014) 358–378. [Google Scholar]
  22. C. Dapogny, R. Estevez, A. Faure and G. Michailidis, Shape and topology optimization considering anisotropic features induced by additive manufacturing processes, Hal Preprint: https://hal.archives-ouvertes.fr/hal-01660850/ (2017). [Google Scholar]
  23. C. Dapogny, A. Faure, G. Michailidis, G. Allaire, A. Couvelas and R. Estevez, Geometric constraints for shape and topology optimization in architectural design. Comput. Mech. 59 (2017) 933–965. [Google Scholar]
  24. G. David and S. Semmes, Uniform rectifiability and singular sets. Ann. Inst. Henri Poincaré (C) Non Linear Anal. 13 (1996) 383–443. [CrossRef] [Google Scholar]
  25. M.C. Delfour and J.P. Zolésio, Shape analysis via distance functions. J. Funct. Anal. 123 (1994) 129–201. [Google Scholar]
  26. M.C. Delfour and J.-P. Zolesio, Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization. InVol. 22. SIAM (2011). [Google Scholar]
  27. T.K. Dey and W. Zhao, Approximate medial axis as a voronoi subcomplex.In: Proceedings of the Seventh ACM Symposium on Solid Modeling and Applications. ACM (2002) 356–366. [Google Scholar]
  28. R.J. DiPerna and P.-L. Lions, Ordinary differential equations, transport theory and sobolev spaces. Invent. Math. 98 (1989) 511–547. [Google Scholar]
  29. D.A. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods. In Vol. 69 Springer Science & Business Media (2011). [Google Scholar]
  30. J. Duoandikoetxea, Forty years of muckenhoupt weights. In: Function Spaces and Inequalities. Matfyzpress, Praga (2013) 23–75. [Google Scholar]
  31. B. Erem and D.H. Brooks, Differential geometric approximation of the gradient and hessian on a triangulated manifold. In: Vol. 504(2011). [Google Scholar]
  32. A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements. In Vol. 159. Springer Science & Business Media (2013). [Google Scholar]
  33. W.D. Evans, Weighted sobolev spaces. Bull. London Math. Soc. 18 (1986) 220–221. [CrossRef] [Google Scholar]
  34. L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions. In: Studies in Advanced Mathematics. CRC Press (1992). [Google Scholar]
  35. F. Feppon and P.F.J. Lermusiaux, A geometric approach to dynamical model order reduction. SIAM J. Matrix Anal. App. 39 (2018) 510–538. [CrossRef] [Google Scholar]
  36. F. Feppon, G. Allaire, F. Bordeu, J. Cortial and C. Dapogny, Shape optimization of a coupled thermal fluid-structure problem in a level set mesh evolution framework. Hal Preprint: https://hal.archives-ouvertes.fr/hal-01686770/ (2018). [Google Scholar]
  37. F. Feppon, G. Allaire, and C. Dapogny, Null space gradient flows for constrained optimization with applications to shape optimization. Hal Preprint: https://hal.archives-ouvertes.fr/hal-01972915/ (2019). [Google Scholar]
  38. J.K. Guest, Imposing maximum length scale in topology optimization. Struct. Multi. Optim. 37 (2009) 463–473. [CrossRef] [Google Scholar]
  39. F. Hecht, New development in freefem++. J. Numer. Math. 20 (2013) 251–265. [Google Scholar]
  40. A. Henrot and M. Pierre, Variation et optimisation de formes: une analyse géométrique. In Vol 48. Springer Science & Business Media (2006). [Google Scholar]
  41. M. Jensen, Discontinuous Galerkin methods for Friedrichs systems with irregular solutions. Ph.D. thesis, University of Oxford (2005). [Google Scholar]
  42. T. Krainer and B.W. Schulze, Weighted Sobolev Spaces, Springer (1985). [Google Scholar]
  43. A. Kufner and B. Opic, How to define reasonably weighted sobolev spaces. Commentationes Math. Univ. Carolinae 25 (1984) 537–554. [Google Scholar]
  44. S. Lang, Fundamentals of Differential Geometry. In Vol. 191. Springer Science & Business Media (2012). [Google Scholar]
  45. Y.Y. Li and L. Nirenberg, The distance function to the boundary, finsler geometry, and the singular set of viscosity solutions of some hamilton-jacobi equations. Commun. Pure Appl. Math. 58 (2005) 85–146. [Google Scholar]
  46. J. Liu and Y. Ma, A survey of manufacturing oriented topology optimization methods. Adv. Eng. Softw. 100 (2016) 161–175. [Google Scholar]
  47. J. Luo, Z. Luo, S. Chen, L. TongandM.Y. Wang, A new level set method for systematic design of hinge-free compliant mechanisms. Comput. Methods Appl. Mech. Eng. 198 (2008) 318–331. [Google Scholar]
  48. C. Mantegazza, A.C. Mennucci, Hamilton-Jacobi equations and distance functions on riemannian manifolds. Appl. Math. Optim. 47 (2003) 1–25. [Google Scholar]
  49. M. Meyer, M. Desbrun, P. Schröder and A.H. Barr, Discrete differential-geometry operators for triangulated 2-manifolds. In: Visualization and Mathematics III. Springer (2003) 35–57. [CrossRef] [Google Scholar]
  50. G. Michailidis, Manufacturing constraints and multi-phase shape and topology optimization via a level-set method. Ph.D. thesis, Ecole Polytechnique (2014). [Google Scholar]
  51. F. Murat and J. Simon, Etude de problèmes d’optimal design. Springer (1975) 54–62. [Google Scholar]
  52. E. Peynaud, Rayonnement sonore dans un écoulement subsonique complexe en régime harmonique: analyse et simulation numérique du couplage entre les phénomènes acoustiques et hydrodynamiques. Ph.D. thesis, Toulouse, INSA (2013). [Google Scholar]
  53. J.C. Robinson, Infinite-dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors. In Vol. 28. Cambridge University Press, Cambridge (2001). [Google Scholar]
  54. W. Rudin, Real and Complex Analysis. Tata McGraw-Hill Education, New York, NY (2006). [Google Scholar]
  55. S. Rusinkiewicz, Estimating curvatures and their derivatives on triangle meshes. In: Proceedings. 2nd International Symposium on 3D Data Processing, Visualization and Transmission, 2004. 3DPVT 2004. IEEE (2004) 486–493. [Google Scholar]
  56. J. Schropp and I. Singer, A dynamical systems approach to constrained minimization. Numer. Funct. Anal. Optim. 21 (2000) 537–551. [Google Scholar]
  57. J.A. Sethian, A fast marching level set method for monotonically advancing fronts. Proc. Nat. Acad. Sci. 93 (1996) 1591–1595. [CrossRef] [Google Scholar]
  58. J. Sokolowski and J.-P. Zolésio, Introduction to shape optimization. In: Vol. 16 of Springer Series in Computational Mathematics, Springer-Verlag, Berlin (1992). [CrossRef] [Google Scholar]
  59. L. Tartar, An Introduction to Sobolev Spaces and Interpolation Spaces. Vol. 3. Springer Science & Business Media (2007). [Google Scholar]
  60. B.O. Turesson, Nonlinear Potential Theory and Weighted Sobolev Spaces. Springer (2007). [Google Scholar]
  61. M.Y. Wang, X. Wang and D. Guo, A level set method for structural topology optimization. Comput. Methods Appl. Mech. Eng. 192 (2003) 227–246. [Google Scholar]
  62. G.H. Yoon, S. Heo and Y.Y. Kim, Minimum thickness control at various levels for topology optimization using the wavelet method. Int. J. Solids Struct. 42 (2005) 5945–5970. [Google Scholar]
  63. H. Zhao, A fast sweeping method for eikonal equations. Math. Comput. 74 (2005) 603–627. [Google Scholar]

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