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The topological asymptotic for the Helmholtz equation. (English) Zbl 1051.49029
Summary: The aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a functional with respect to the creation of a small hole in the domain. In this paper such an expansion is obtained for the Helmholtz equation with a Dirichlet condition on the boundary of a circular hole. Some applications of this work to waveguide optimization are presented.
MSC:
49Q10Optimization of shapes other than minimal surfaces
49Q12Sensitivity analysis
78A50Antennas, wave-guides
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation