Mimetic Finite Difference Method for Shape Optimization Problems

Abstract

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Higher-Order Moving Mesh Methods for PDE-Constrained Shape Optimization

“…Here, we consider approximation by means of finite elements, which has become the most popular choice for PDE-constrained shape optimization due to its flexibility for engineering applications. Nevertheless, it is worth mentioning that alternatives based on other discretizations have also been considered [6,9,18,43].…”

“…The key tool is the derivative of the shape functional J with respect to shape perturbations. To give a more precise description, let us first introduce the operator (6) J :…”

“…A shape functional J is said to be shape differentiable (in T (Ω 0 )) if the corresponding functional (6) is Fréchet differentiable (in T ), that is, if (8) defines a linear continuous operator on…”