Mathematics and Applications Seminar by Dr. Carlos Borges

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

Mathematics and Applications Seminar 
11:00am - 12:00pm, Friday, Mar 10, 2023 
MSB 318 

Speaker: 
Dr. Carlos Borges 
Department of Mathematics 
University of Central Florida

Title: On the Robustness of Inverse Scattering for Penetrable, Homogeneous Objects with Complicated Boundary 

Abstract: 
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. 

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The UCF Mathematics and Applications Seminar, which takes place every Friday from 11am to 12pm 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.

https://sciences.ucf.edu/math/seminar/mathematics-and-applications-seminar

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