Optimal shape design for Helmholtz/potential flow problem using fictitious domain method

In this paper the implementation of shape optimization techniques based on nonlinear programming for airfoil design is presented. An airfoil profile is designed such that its radar visibility is low but it has some prescribed aerodynamical properties. The combined electromagnetics/flow problem is modeled by Helmholtz equation and potential flow. The state equations are discretized using the finite element method and the resulting linear systems of equations are solved using the fictitious domain method. The geometric design sensitivity analysis needed for the efficient use of nonlinear programming algorithms is performed using analytical expressions for derivatives. Finally, several numerical examples are given.

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