Research Interests

    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

Research Supervision

    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)

  • Adaptive isogeometric method for incompressible flows (Manuscript in prepration)

  • Isogeometric finite element solver for thermal stress analysis (Manuscript in prepration)