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The Research Seminar is a weekly space that focuses on various areas of applied mathematics, with special emphasis on Mathematical Optimization and Modeling. The main objective is to share the research results of the Modemat and put the researchers of the Center in contact with academics from all over the world, in person or through virtual platforms. Organizer of the seminar: Sergio González Andrade. To subscribe to the Seminar mailing list or propose a talk in it, please write to: sergio.gonzalez@epn.edu.ec

Shape optimization approach for sharp-interface reconstructions in inverse problems.

Shape optimization approach for sharp-interface reconstructions in inverse problems.

By Antoine Laurain, profesor de la Universidad de Sao Paulo, Brasil

Seminar Date: 2021-02-18

Working within the class of piecewise constant models, inverse problems can be recast as shape optimization problems where the discontinuity interface is the unknown. The sensitivity analysis of the cost functional relies on shape optimization techniques and in particular on the concept of shape derivatives. I will show several recent developments including a shape-Lagrangian approach for point measurements, and distributed shape derivatives for geometries with low regularity. Numerical results based on a level set approach will be presented for the inverse problems of electrical impedance tomography and full waveform inversion

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