Office: UNA 110
My research interests are focused on the development, theoretical analysis and implementation of efficient algorithms in view of their application to the simulation of problems of practical interest. My specialty is on the use of Discontinuous Galerkin Finite Element Methods (DG-FE) methods for the numerical solution of problems arising in biomedical and material sciences. Specifically, I am interested in the development and analysis of high order numerical schemes that accurately and efficiently resolve the solution to non linear equations like Cahn-Hilliard type equations, arising in models describing biological growth e.g. cancerous tumors and phase separation. Adaptive mesh refinement, (theoretical) error analysis and energy stability via convex splitting are also being addressed in my work. For the solution of the resulting algebraic (nonlinear) systems efficient solvers based on multigrid are designed.
The development of hybrid discrete cellular automata systems (HD-CA) by coupling linear and non-linear reaction diffusion partial differential equations with discrete (stochastic) cellular automata systems is also a part of my work. I utilize hybrid discrete systems to derive constitutive relationships and study phenomena in tissue engineering, cancer modeling, and evolutionary game theory. Another aspect of my research is related to the study of the various mechanisms governing the dorsal closure in the drosophila embryo through the development of individual based mechanistic models. The dorsal closure morphogenesis closely resembles the wound healing process in animal and human tissue, thus its study is of great importance.
I am looking for motivated students with love for mathematics that are interested in doing research. Ask me for more details!!
Hybrid Discrete Systems
Computational Fluid Dynamics