My research interests are related to Numerical Analysis and Scientific Computing. In recent years, I have focused on design and analysis of highly efficient and robust numerical methods for solving differential equations.
In particular, my research work can be characterized by the following keywords:
- Isogeometric analysis
- Finite element methods
- Error estimation and adaptivity
- Compatible discretization of PDEs
- Numerical analysis of singular perturbation problems
- Domain decomposition methods
- Deep Learning
- Medical image processing
I have supervised many students in past. Currently, I am supervising:
Abdullah Abdulhaque (Ph.D. student, NTNU Norway)Adaptive Isogeometric Methods for Boussinesq Problems, Norwegian University of Science and Technology, Norway.
Michael Lanier (CofC undergraduate student)An Automated System for Polyp Detection in Wireless Capsule Endoscopy Images based on Deep Learning, SURF Project 2018, College of Charleston, South Carolina.
Tea Luu (CofC undergraduate student)Numerical Techniques for Nematic Liquid Crystal, SURF Project 2016, College of Charleston, South Carolina.
Overview of Current Research
Characterization of T-Splines with reduced continuity order PDF
Error estimator using Serendipity pairing of approximation spaces with LR B-splines PDF
Divergence-conforming discretization of Lid-driven cavity flow problem PDF
Goal oriented error estimation in isogeometric analysis (Manuscript in prepration)
Isogeometric finite element solver for thermal stress analysis (Manuscript in prepration)