Parametric free-form shape design with PDE models and reduced basis method

We present a coupling of the reduced basis methods and free-form deformations for shape optimization and design of systems modelled by elliptic PDEs. The free-form deformations give a parameterization of the shape that is independent of the mesh, the initial geometry, and the underlying PDE model. The resulting parametric PDEs are solved by reduced basis methods. An important role in our implementation is played by the recently proposed empirical interpolation method, which allows approximating the non-affinely parameterized deformations with affinely parameterized ones. These ingredients together give rise to an efficient online computational procedure for a repeated evaluation design environment like the one for shape optimization. The proposed approach is demonstrated on an airfoil inverse design problem.


Published in:
Computer Methods in Applied Mechanics and Engineering, 199, 23-24, 1583-1592
Year:
2010
Publisher:
Elsevier
ISSN:
0045-7825
Keywords:
Note:
EPFL MATHICSE report 01.2010
Laboratories:




 Record created 2010-01-18, last modified 2018-03-17

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