ESAIM Control Optimisation and Calculus of Variations · 2009 · 26 citations · 14 references
Numerical AnalysisMathematical ProgrammingEngineeringVariational AnalysisComputational MechanicsEnergy MinimizationMesh OptimizationSingle MeshShape OptimizationMaterials OptimizationApproximation TheoryLinear OptimizationGeometric ModelingSteepest Descent MethodErsatz Material ApproximationInverse ProblemsConstructive ApproximationFinite Element MethodNatural SciencesApproximation Method
The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a ersatz material approximation [Allaire et al., J. Comput. Phys. 194 (2004) 363–393], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic error committed by using the ersatz material approximation and, on a model case, explain that they amplifies instabilities by a second order analysis of the objective function.
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