A survey on level set methods for inverse problems and optimal design

By Martin Burger, Stanley J. Osher. European journal of applied mathematics, 2005

319 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/22eea9c9a4aeb9170c2fd01e2976797a64d6dd63

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In Civil and Structural Engineering

In Computational Mechanics

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Citations in the corpus

An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions (2018, background): “More details about the current development of various topology optimization approaches, especially the level set-based methods, can refer to the following review articles (Burger and Osher 2005; Gain and Paulino 2013; Dijk et al. 2013; Sigmund and Maute 2013; Deaton and Grandhi 2014).”
Topology optimization approaches (2013, methodology): “To ensure that the evolution of the level set function is efficiently driven by the shape sensitivities, the gradients of the level set function should be uniform along the interface, for example |∇φ| ≈ 1 (Burger and Osher 2005).”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “For more comprehensive discussion of level set methods for topology optimization, we refer interested readers to the review articles of Burger and Osher (2005) and most recently van Dijk et al.”
Spatially adaptive techniques for level set methods and incompressible flow (2006, background): “In particular, several attempts have been made at extending the method to handle objects of higher codimension [9, 48, 17], there has been interesting work on inverse problems [10], and a few authors have combined level sets with finite element methods in order to accurately describe cracks and frac”
Detection of material interfaces using a regularized level set method in piezoelectric structures (2016, methodology): “A survey on application of level set methods in inverse problems and optimal design can be found in Burger and Osher [2].”
Level set methods for inverse scattering (2006, methodology): “For brevity we simply refer here to the discussions presented in [4, 160, 15, 26, 27, 29, 71, 85, 93, 141, 153] and the many further references therein.”
A piecewise constant level set method for elliptic inverse problems (2007, background): “In the recent surveys [29,5], some more detailed information about these approaches and references can be found.”