On Convergence in Elliptic Shape Optimization

A Level Set Based Shape Optimization Method for an Elliptic Obstacle Problem

In this paper we construct a level set method for an elliptic obstacle problem, which can be reformulated as a shape optimization problem. We provide a detailed shape sensitivity analysis for this reformulation and a stability result for the shape Hessian at the optimal shape. Using the shape sensitivities we construct a geometric gradient flow, which can be realized in the context of level set...

Airfoil Shape Optimization with Adaptive Mutation Genetic Algorithm

An efficient method for scattering Genetic Algorithm (GA) individuals in the design space is proposed to accelerate airfoil shape optimization. The method used here is based on the variation of the mutation rate for each gene of the chromosomes by taking feedback from the current population. An adaptive method for airfoil shape parameterization is also applied and its impact on the optimum desi...

A Penalization and Regularization Technique in Shape Optimization Problems

We consider shape optimization problems, where the state is governed by elliptic partial differential equations (PDE). Using a regularization technique, unknown shapes are encoded via shape functions, turning the shape optimization into optimal control problems for the unknown functions. The method is studied for elliptic PDE to be solved in an unknown region (to be optimized), where the regula...

The Effects of Shape Parameterization on the Efficiency of Evolutionary Design Optimization for Viscous Transonic Airfoils

The effect of airfoil shape parameterization on optimum design and its influence on the convergence of the evolutionary optimization process is presented. Three popular airfoil parametric methods including PARSEC, Sobieczky and B-Spline (Bezier curve) are studied and their efficiency and results are compared with those of a new method. The new method takes into consideration the characteristics...

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)