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Numerical minimization of eigenmodes of a membrane with respect to the domain. (English) Zbl 1076.74045

Summary: We introduce a numerical approach adapted to the minimization of eigenmodes of a membrane with respect to the domain. This method is based on a combination of the level set method of S. Osher and J. A. Sethian [J. Comput. Phys. 79, No. 1, 12–49 (1988; Zbl 0659.65132)] with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.

MSC:

74P10 Optimization of other properties in solid mechanics
74K15 Membranes
65K10 Numerical optimization and variational techniques
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
49Q10 Optimization of shapes other than minimal surfaces

Citations:

Zbl 0659.65132
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References:

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