Journal of Applied Mathematics and Physics

Volume 5, Issue 2 (February 2017)

ISSN Print: 2327-4352   ISSN Online: 2327-4379

Google-based Impact Factor: 0.70  Citations  

The Technique of the Immersed Boundary Method: Application to Solving Shape Optimization Problem

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DOI: 10.4236/jamp.2017.52030    1,305 Downloads   2,198 Views  Citations
Author(s)

ABSTRACT

We present a numerical method based on genetic algorithm combined with a fictitious domain method for a shape optimization problem governed by an elliptic equation with Dirichlet boundary condition. The technique of the immersed boundary method is incorporated into the framework of the fictitious domain method for solving the state equations. Contrary to the conventional methods, our method does not make use of the finite element discretization with obstacle fitted meshes. It conduces to overcoming difficulties arising from re-meshing operations in the optimization process. The method can lead to a reduction in computational effort and is easily programmable. It is applied to a shape reconstruction problem in the airfoil design. Numerical experiments demonstrate the efficiency of the proposed approach.

Share and Cite:

Rao, L. and Chen, H. (2017) The Technique of the Immersed Boundary Method: Application to Solving Shape Optimization Problem. Journal of Applied Mathematics and Physics, 5, 329-340. doi: 10.4236/jamp.2017.52030.

Cited by

[1] Numerical solution for a nonlinear obstacle problem
Journal of Nonlinear Sciences and Applications, 2018
[2] Numerical solution for a nonlinear obstacle problem.
2018

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