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Mathematical Modeling and Optimization of Complex Structures pp 43–57Cite as

An Automatic Differentiation Based Approach to the Level Set Method

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Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 40))

Abstract

This paper discusses an implementation of the parametric level set method. Adjoint approach is used to perform the sensitivity analysis, but contrary to standard implementations, the state problem is differentiated in its discretized form. The required partial derivatives are computed using tools of automatic differentiation, which avoids the need to derive the adjoint problem from the governing partial differential equation. The augmented Lagrangian approach is used to enforce volume constraints, and a gradient based optimization method is used to solve the subproblems. Applicability of the method is demonstrated by repeating well known compliance minimization studies of a cantilever beam and a Michell type structure. The obtained topologies are in good agreement with reference results.

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Acknowledgments

The author was financially supported by Academy of Finland, grant #257589.

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Authors and Affiliations

  1. Department of Mathematical Information Technology, University of Jyväskylä, 35 (Agora), 40014, Jyväskylä, Finland

    Jukka I. Toivanen

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  1. Jukka I. Toivanen
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Correspondence to Jukka I. Toivanen .

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Editors and Affiliations

  1. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Pekka Neittaanmäki

  2. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Sergey Repin

  3. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Tero Tuovinen

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Toivanen, J.I. (2016). An Automatic Differentiation Based Approach to the Level Set Method. In: Neittaanmäki, P., Repin, S., Tuovinen, T. (eds) Mathematical Modeling and Optimization of Complex Structures. Computational Methods in Applied Sciences, vol 40. Springer, Cham. https://doi.org/10.1007/978-3-319-23564-6_4

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  • DOI: https://doi.org/10.1007/978-3-319-23564-6_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23563-9

  • Online ISBN: 978-3-319-23564-6

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