Research and Software

Publications and Preprints

• Manaswinee Bezbaruah, Matthias Maier, Winnifried Wollner

Shape optimization of optical microscale inclusions (Submitted, 2023)

Current Work

I am interested in Finite Element simulation of two-scale and multi-scale phenomena. More recently, I have been working on Time Harmonic Maxwell's equations and the multiscale phenomena observed in Surface Plasmon Polaritons (SPPs). SPPs are a type of surface wave that can be guided along an interface the same way light can be guided by optical fibers, and they are created due to special material properties of inert metals and graphene. 

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.

Another direction that I am interested in is the shape and eigenvalue optimization problems arising in the context of homogenization of novel optical devices. We investigate the well-posedness, solution spaces, and numerical solution of the cell problem arising as the effective tensor of the Time Harmonic Maxwell's Equations. In order to do this, we deform the surface using an Arbitrary Lagrangian Eulerian (ALE) transformation, which we then optimize using a duality argument.  https://arxiv.org/abs/2306.13248

Past Work

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