Research and Software

Publications and Preprints

• Manaswinee Bezbaruah, Matthias Maier, Winnifried Wollner

Shape optimization of optical microscale inclusions

SIAM Journal on Scientific Computing (Accepted, 2024)

• T. Mattson, M. Bezbaruah, M. Maier, S. McMillan, M. Pelletier , E. Welch, T. Davis 

Indexed Binary Operations in the GraphBLAS

IEEE HPEC [Conference Proceeding], (Accepted, 2024)

Current Work

My doctoral research focuses on shape optimization of nanoscale optical metamaterials with the objective of fine-tuning their optical properties. These materials have a wide range of applications, from biomedical devices to photovoltaic batteries. They exhibit a variety of striking optical phenomenon that are unlike the classical behavior of electromagnetic waves. The ability to precisely tailor these properties through shape optimization offers profound implications for enhancing performance of these materials. As a result, I am motivated to describe, design, and tune the optical properties of these materials using mathematical models and computational tools. 

I created a robust 2D solver for the Time Harmonic Maxwell's equations with Dr. Maier to add as an example step on the Finite Element library deal.ii step-81. Following are some images of our simulated SPP.

The above simulation is of the forward problem where we compute the permittivity of a plasmonic material with a certain geometry of the plasmonic material. The shape optimization process solves the inverse problem of finding a geometry that let's us acheive a target geometry. Detailed discussion of the PDE-constrained optimization problem is available here: https://arxiv.org/pdf/2306.13248. Following is a simulation of the shape optimization algorithm developed using deal.II and DOpElib (our source code is publicly available here)

Additionally, I am interested in making this shape optimization algorithm more efficient. I am approaching this in two ways:

1. Using the related eigenvalue problem to formulate a frequency dependent cost function. This reduces the number of variables the optimization algorithm depends on.

2. Using parallel and multithreaded methods to assemble the finite element matrices. I am developing methods to assemble sparse matrices from their sparsity pattern using IndexBinaryOps in GraphBLAS.

Past Work

Previously, I was interested in Mathematical Biology and Evolutionary Models. Here are some presentations: