Incorporating topological derivatives into level set methods

By Martin Burger, Benjamin Hackl, Wolfgang Ring. 2004

386 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/9b473470b63ac0a76abddf4c80f20d06c1c37a1d

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In Civil and Structural Engineering

In Computational Mechanics

Citations in the corpus

A multi-material level set-based topology and shape optimization method (2015, methodology): “For the single-material design problems, some alternative level set methods have also been proposed to improve the optimization behavior, to save computational cost of the optimization process, or to achieve special objective functions [30–36].”
Minimum stress optimal design with the level set method. (2008, methodology): “Let us mention, for example, works on its coupling with the topological gradient for holes nucleation [3], [13], [41], or velocity/derivative regularization [20].”
A binary level set model and some applications to Mumford-Shah image segmentation (2006, background): “” Alternatively, topological derivatives can be used in order to identify complex geometries in level set methods [8], [44].”
Structural Shape and Topology Optimization Using an Implicit Free Boundary Parametrization Method (2006, methodology): “…equation is solved under a strict condition for numerical stability and reinitialization is applied to the level set function to ensure its regularity [Sethian (1999); Tsai and Osher (2003); Allaire, Gournay, Jouve, and Toader (2004); Burger, Hackl, and Ring (2004); Wang and Wang (2005d)].”
A multi-material topology optimization algorithm based on the topological derivative (2019, methodology): “As an alternative to choosing a perforated initial design in the level set method, a coupling of the Hamilton-Jacobi equation, which uses shape sensitivities, with the topological derivative was proposed in [ 3, 10 ] .”
Shape optimization with a level set based mesh evolution method (2014, positive): “To circumvent this difficulty, the works [8, 22], based on results of [37, 41, 61], proposed to add an altogether different information to the shape optimization process, namely that of the sensitivity of a shape with respect to the nucleation of a small hole, which we briefly outline now.”
Connections between topological sensitivity analysis and material interpolation schemes in topology optimization (2011, background): “Therefore, the topological sensitivity may be advantageously combined with level set methods (Allaire et al. 2005; Amstutz and Andrä 2006; Burger et al. 2004).”
A new algorithm for topology optimization using a level-set method (2006, methodology): “Unlike other algorithms which have been developed on the same purpose [3, 14, 31], we have completely abandoned the Hamilton-Jacobi equation, getting quite far from the usual notion of “level-set method”.”
A level set method for structural shape and topology optimization using radial basis functions (2009, background): “Furthermore, in most conventional level set methods, the final design is generally dependent on the initial guess because no mechanism is included to create new holes inside the material domain [24].”
Level set methods for inverse scattering (2006, methodology): “Moreover, we again refer to [10, 28, 76, 78, 87, 145] and the further references given there for numerical approaches which focus on topology changes during the reconstruction.”