The Topological Asymptotic for the Helmholtz Equation
Bessem Samet, Samuel Amstutz, Mohamed Masmoudi · SIAM Journal on Control and Optimization · 2003
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.