4.7 Article

On a numerical approach for solving some geometrical shape optimization problems in fluid mechanics

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On numerical study of constrained coupled shape optimization problems based on a new shape derivative method

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Summary: In this article, a numerical method for approximating coupled shape optimization problems is presented. The method involves minimizing a general volume cost functional subject to coupled boundary value problems using a Neumann boundary transmission condition. The existence of the shape derivative of the cost functional is shown and expressed using support functions based on a new formula for shape derivative on a family of convex domains. The dual reciprocity boundary element method is employed for numerical discretization to avoid the remeshing task required for the finite element method. Numerical results based on the gradient method demonstrate the efficiency of the proposed approach.

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