ORCID
0009-0000-0828-6478
Keywords
Inverse Scattering Problems, Flexural Waves, Multifrequency, Computational Methods, Generalized Impedance Boundary Conditions, Thin Coating
Subject Categories
Applied Mathematics | Mathematics
Abstract
This dissertation develops efficient computational methods for two inverse scattering problems arising in wave propagation, with applications to thin coated obstacles and flexural waves in thin elastic plates. The first part addresses an inverse obstacle scattering problem for a perfectly conducting domain coated with a thin penetrable layer of variable thickness. The coating is modeled using generalized impedance boundary conditions, reducing the computational cost relative to the full transmission model. The boundary shape and impedance function are recovered from multifrequency scattered-field data using a Gauss--Newton optimization framework combined with boundary integral equation methods. The second part considers a volumetric inverse scattering problem for flexural waves governed by the biharmonic operator. The forward problem is reformulated through a Lippmann--Schwinger volume integral equation, and the spatially varying contrast is reconstructed using an optimization framework based on the steepest descent method. Numerical experiments demonstrate accurate and stable reconstructions and highlight the effectiveness of using multifrequency data.
Completion Date
2026
Semester
Summer
Committee Chair
Cardoso Borges, Carlos
Degree
Doctor of Philosophy (Ph.D.)
College
College of Sciences
Department
School of Data, Mathematical, and Statistical Sciences
Format
Document Type
Dissertation
Language
English
Release Date
8-15-2027
STARS Citation
Vasconcellos Viana, Isabela, "Computational Methods for Multifrequency Inverse Scattering Problems: From Thin Coating Recovery to Flexural Wave Reconstruction" (2026). Graduate Studies Theses and Dissertations 2026. 371.
https://stars.library.ucf.edu/gradstudies_etd_2026/371
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