A penalization approach in shape optimization | Zendy

Dan Tiba | Zendy

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A penalization approach in shape optimization

Author(s) -

Dan Tiba

Publication year - 2018

Publication title -

doaj (doaj: directory of open access journals)

Language(s) - English

DOI - 10.1478/aapp.961a8

Subject(s) - parametrization (atmospheric modeling) , mathematical optimization , domain (mathematical analysis) , shape optimization , optimization problem , mathematics , variable (mathematics) , hamiltonian (control theory) , boundary (topology) , computer science , boundary value problem , mathematical analysis , engineering , physics , structural engineering , quantum mechanics , finite element method , radiative transfer

We introduce a new approximation technique in general shape optimization problems, involving unknown/variable domains, that penalizes the given boundary condition in the cost functional. The essential technical ingredient is provided by the implicit parametrization theorem, using Hamiltonian systems, recently developed by the author and his collaborators. The method is of fixed domain type and reduces the original problem to a distributed control problem.

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