Forward Scattering for Thin Coated Domains: Numerical Solution Using Generalized Impedance Boundary Conditions

May 2024 - July 2024

Principle Investigator: Dr. Carlos Borges
Institution: University of Central Florida
Department: Mathematics

Research Focus:

This research project aimed to create a more efficient solver for the forward scattering problem, for objects with a thin coating. This involves figuring out the scattered waves created when a wave hits an impenetrable obstacle that's covered by a thin, penetrable layer. This has many practical applications, such as designing coatings that can hide objects from radar in the defense industry or creating special thin films for lenses to change their properties.

Responsibilities:

In the beginning, I read through many papers in order to familiarize myself with the topic of research. I then presented my knowledge to my PI, Dr. Carlos Borges, along with my partner in the REU. During this time we also attended various workshops and seminars relating to computational mathematics.

Finally, we began work on the project itself, and in order to create the solver we modified Matlab code that was meant to solve the forward problem for impenetrable objects without a thin layer. In order to make the solver less costly computationally, we simplified the original forward problem for an object with a thin coating, called the transmission problem, using General Impedance Boundary Conditions (GIBCs). These GIBCs simplified the wave equation which calculated the wave as it travelled through the thin layer, instead turning this complex equation into simpler boundary conditions. These GIBCs were then used in the code to replace the original Dirichlet boundary condition. This approximation was called the impedance problem, and we compared its results to the "true solution", aka the transmission problem. We used order 1 and order 2 GIBCs, since the higher the order of GIBC the more complex the condition was. The GIBCs calculated ranged from orders 0-4, however 0 was too simple and 3-4 too complex for the approximation.

In our final results, we found that GIBC order 2 was a nearly perfect approximation. Then after getting these results, we presented our project in a poster symposium at UCF.

My Research Poster