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A Unified Discrete–Continuous Sensitivity Analysis Method for Shape Optimization

  • Martin BerggrenEmail author
Chapter
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 15)

Summary

Boundary shape optimization problems for systems governed by partial differential equations involve a calculus of variation with respect to boundary modifications. As typically presented in the literature, the first-order necessary conditions of optimality are derived in a quite different manner for the problems before and after discretization, and the final directional-derivative expressions look very different. However, a systematic use of the material-derivative concept allows a unified treatment of the cases before and after discretization. The final expression when performing such a derivation includes the classical before-discretization (“continuous”) expression, which contains objects solely restricted to the design boundary, plus a number of “correction” terms that involve field variables inside the domain. Some or all of the correction terms vanish when the associated state and adjoint variables are smooth enough.

Keywords

Topology Optimization Shape Optimization Directional Derivative Adjoint Equation Discrete Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Computing ScienceUmeå UniversityUmeåSweden

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