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Level set methods for optimization problems involving geometry and constraints. I: Frequencies of a two-density inhomogeneous drum. (English) Zbl 1056.74061

From the summary: Many problems in engineering design involve optimizing the geometry to maximize a certain design objective. Geometrical constraints are often imposed. In this paper, we use the level set method, the variational level set calculus and the projected gradient method to construct a simple numerical approach for problems of this type. We apply this technique to a model problem involving a vibrating system whose resonant frequency or whose spectral gap is to be optimized subject to constraints on geometry.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
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