Fast level set based algorithms using shape and topological sensitivity information

A framework for descent algorithms using shape as well as topological sensitivity information is introduced. The concept of gradient-related descent velocities in shape optimization is defined, a corresponding algorithmic approach is developed, and a convergence analysis is provided. It is shown that for a particular choice of the bilinear form involved in the definition of gradient-related directions a shape Newton method can be obtain. The level set methodology is used for representing and updating the geometry during the iterations. In order to include topological changes in addition to merging and splitting of existing geometries, a descent algorithm based on topological sensitivity is proposed. The overall method utilizes the shape sensitivity and topological sensitivity based methods in a serial fashion. Finally, numerical results are presented

Electrical impedance tomography: from topology to shape

A level set based shape and topology optimization approach to electrical impedance tomography (EIT) problems with piecewise constant conductivities is introduced. The proposed solution algorithm is initialized by using topological sensitivity analysis. Then it relies on the notion of shape derivatives to update the shape of the domains where conductivity takes different values