Research Interests

Research Interests:

My research interests cover an intersection between Applied Mathematics & Engineering. I work on numerical methods for ordinary and partial differential equations which arise in diverse engineering problems from different fields, such as: Computational Mechanics, Fracture Mechanics, Material Science, Computer Vision, and Bioengineering.

Research Topics:

1- Research in Computational Mathematics / Ordinary and Partial Differential Equations: 

• Immersed Finite Elements for Interface Problems

• Finite Elements Method for Second Order Elliptic Equations

• Higher Degree Immersed Finite Elements

• Finite Difference Method

• Efficient Numerical Methods for Nonlinear Differential Equations

2- Research in Computational Mechanics:

• Fracture Mechanics of Functionally Graded Materials

• Contact Problems involving Functionally Graded Piezoelectric Materials

• Numerical Solutions to Singular Integral Equations

3- Research in Computer Vision and Scientific Visualization: 

• Partial Differential Equations for Image Segmentation and Contour Detection

• Mathematical Modeling for Texture Analysis and Synthesis

• Computational Methods in Computer Vision

4- Research in Mathematical Biology and Bioengineering:

• Numerical Analysis and Study of Infectious Diseases

• Dynamical Systems arising in Infectious Diseases Modeling