References
- A
dams , T., Giani , S.and Coombs , W. (2016) Topology optimisation using level set methods and the discontinuous Galerkin method. In: Proc. of the 24th UK Conf. of the Association for Computational Mechanics in Engineering (ACME-UK), Cardi University, Cardi : 6–9. - A
llaire , G.,de Gournay , F., Jouve , F.and Toader , A. M. (2005) Structural optimization using topological and shape sensitivity via a level set method. Control Cybernet. 34, 59–80. - A
llaire , G., Jouve , F.and Toader , A. M. (2004) Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194 363–393. - A
llaire , G., Dapogny , C.and Jouve , F. (2021) Shape and topology optimization. Handb. Numer. Anal. 22, 1–132. - A
rnold , D. N., Brezzi , F., Cockburn , B.and Marini , L. D. (2002) Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 1749–1779. - B
endsøe , M. P.and Sigmund , O. (2003) Topology Optimization: Theory, Methods, and Applications. Springer, Berlin. - B
uhl , T., Pedersen , C.and Sigmund , O. (2000) Sti ness design of geometrically nonlinear structures using topology optimization. Struct. Multidiscip. Optim. 19 (2) 93–104. - C
iarlet , P. G. (1988) Mathematical Elasticity, Three-Dimensional Elasticity, vol. I. North-Holland, Amsterdam. - D
apogny , C.and Frey , P. (2010) Computation of the signed distance function to a discrete contour on adapted triangulation. Calcolo, 49 1-27. - E
rn , A.and Guermond , J. L. (2006) Discontinuous Galerkin methods for Friedrichs’ systems. I. General theory. SIAM J. Numer. Anal. 44, 753–778. - E
vgrafov , A. (2018) Discontinuous Petrov-Galerkin methods for topology optimization. In: H. Rodrigues et al., eds., Proceedings of the 6th International Conference on Engineering Optimization. EngOpt 2018. Springer, Cham. - F
ulmanski , P., Laurain , A., Scheid , J.-F.and Soko lowski , J. (2008) Level set method with topological derivatives in shape optimization. Int. J. Comput. Math. 85, 1491–1514. - G
anghoffer , J. F., Plotnikov , P. I.and Sokolowski , J. (2018) Non-convex model of material growth: mathematical theory. Arch. Rational Mech. Anal. 230, 839–910. - H
ansbo , P.and Larson , M. G. (2022) Augmented Lagrangian approach to deriving discontinuous Galerkin methods for nonlinear elasticity problems. Int. J. Numer. Methods Eng. 123, 4407–4421. - H
echt , F. (2012) New development in FreeFem++. J. Numer. Math. 20, 251–265. - H
owell , L. L. (2001) Compliant Mechanisms. John Wiley & Sons. - K
im , N.-H. (2015) Introduction to Nonlinear Finite Element Analysis. Springer, US. - K
wak , J.and Cho , S. (2005) Topological shape optimization of geometrically nonlinear structures using level set method. Comput. Struct. 83, 2257–2268. - L
aurain , A. (2018) A level set-based structural optimization code using FEniCS. Struct. Multidisc. Optim. 58, 1311–1334. - N
ovotny , A. A.and Soko lowski , J. (2013) Topological Derivatives in Shape Optimization. Springer, Berlin. - N
ovotny , A. A., Soko łowski , J.and Zochowski , A. (2019) Applications of the Topological Derivative Method. Springer, Cham. - O
sher , S.and Sethian , J. A. (1988) Front propagation with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12–49. - Q
ian , M.and Zhu , S. (2022) A level set method for Laplacian eigenvalue optimization subject to geometric constraints. Comput. Optim. Appl. 82, 499–524. - R
ivière , B., Shaw , S., Wheeler , M. F.and Whiteman , J. R. (2003) Discontinuous Galerkin finite element methods for linear elasticity and quasistatic linear viscoelasticity. Numer. Math. 95, 347–376. - S
oko lowski , J.and Zolésio , J. P. (1992) Introduction to Shape Optimization: Shape Sensitivity Analysis. Springer, Heidelberg. - T
an , Y.and Zhu , S. (2023) A discontinuous Galerkin level set method using distributed shape gradient and topological derivatives for multi-material structural topology optimization. Struct. Multidiscip. Optim. 66; Article number: 170. - T
an , Y.and Zhu , S. (2024) Numerical shape reconstruction for a semi-linear elliptic interface inverse problem. East Asian J. Appl. Math. 14, 147–178. - Z
heng , J., Zhu , S.and Soleymani , F. (2024) A new efficient parametric level set method based on radial basis function-finite difference for structural topology optimization. Comput. Struct. 291, 107364. - Z
hu , S., Hu , X.and Wu , Q. (2018) A level set method for shape optimization in semilinear elliptic problems. J. Comput. Phys. 355, 104–120.