TITLE:
The Technique of the Immersed Boundary Method: Application to Solving Shape Optimization Problem
AUTHORS:
Ling Rao, Hongquan Chen
KEYWORDS:
Immersed Boundary Method, Genetic Algorithm, Bezier Curve, Elliptic Dirichlet Boundary Value Problem, Shape Optimization Problem
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.2,
February
15,
2017
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.