Abigail Lin

Abigail Lin

I’m a senior at the University of Florida majoring in Computer Science and minoring in Mathematics, driven by a fascination with how computational methods can unlock new insights in biology and accelerate scientific innovation.

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

May 2024 – July 2024

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

Research Focus

This project aimed to develop a more efficient numerical solver for the forward scattering problem involving objects with thin coatings.
In this context, forward scattering refers to predicting how waves are scattered when they strike an impenetrable obstacle covered by a thin, penetrable layer.

Such problems have important practical applications, including:

  • Radar stealth technology through coating design
  • Optical engineering, such as designing thin films for lenses to modify light transmission and reflection

The goal was to simplify and accelerate the computation of these wave interactions while preserving high accuracy.

Responsibilities

At the start of the research, I conducted a literature review to understand the mathematical background of the project and presented my findings to Dr. Borges and my REU partner.
Throughout the program, we also attended seminars and workshops in computational mathematics to strengthen our theoretical foundation.

For the core of the project, we modified existing MATLAB code that solved the forward scattering problem for impenetrable objects.
To model thin coatings efficiently, we replaced the complex transmission problem with a simplified approach using Generalized Impedance Boundary Conditions (GIBCs).

These GIBCs approximate how waves behave as they pass through thin layers by converting the internal wave equations into simpler boundary conditions on the object’s surface.
We implemented GIBCs of orders 1 and 2, testing their ability to reproduce the results of the true transmission problem.
Our findings showed that second-order GIBCs provided an almost perfect approximation while remaining computationally efficient.

Finally, we presented our results in a poster symposium at the University of Central Florida.

My Research Poster

By me

Wave Scattering Research Poster