Mathematics and Applications Seminar by Dr. Carlos Borges

Friday, March 10, 2023 11 a.m. to noon

Dr. Carlos Borges in the Department of Mathematics will present his work: On the Robustness of Inverse Scattering for Penetrable, Homogeneous Objects with Complicated Boundary.

The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (probes). For a penetrable object with known sound speed, this can be accomplished by treating the boundary alone as an unknown curve. Alternatively, one can treat the entire object as unknown and use a more general volumetric representation, without making use of the known sound speed. Both lead to strongly nonlinear and nonconvex optimization problems for which recursive linearization provides a useful framework for numerical analysis. After extending our shape optimization approach developed earlier for impenetrable bodies, we carry out a systematic study of both methods and compare their performance on a variety of examples. Our findings indicate that the volumetric approach is more robust, even though the number of degrees of freedom is significantly larger. We conclude with a discussion of this phenomenon and potential directions for further research. 

The UCF Mathematics and Applications Seminar, which takes place every Friday from 11 a.m. to 12 p.m. in MSB 318, provides a venue for researchers to present their current work, foster new collaborations, and showcase both foundational mathematics and its applications to graduate and undergraduate students.

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