My research will focus on the modeling and computational difficulties associated with portraying the electrophysiology, mechanics, and electromechanics of the heart. The aim is to develop efficient and robust numerical schemes for models of the cardiac electro-mechanical system with high biophysical accuracy across multiple scales and dimensions. The development of efficient numerical techniques on massively parallel computing technologies is a major challenge that the proposed work aims to address.
My research area is mainly focused on Theoretical and Computational Biophysics which is an interdisciplinary topic . Active systems such as microbes and eukaryotic cellular systems are prototypical biological systems that involve the migration of cells driven by chemical stimuli or some self-generated gradients and moving through interactions with other cells and the extracellular environment. Currently, I am working on investigating and understanding the dynamics of these complex systems leading to a large variety of emerging spatiotemporal orders in the form of spatial patterns, propagating waves, collective motions, and phase separation.
My research primarily focuses on numerical analysis and computational methods applied to nonlinear scalar conservation laws, systems of hyperbolic conservation laws, and conservation laws featuring discontinuous flux functions. These equations are prevalent in a wide range of applications, such as traffic modeling, enhanced oil recovery processes, sedimentation phenomena, and the system of Euler equations describing compressible gas dynamics. The primary aim of my research is to design and analyze efficient high-order computational schemes specifically tailored to address nonlinear problems of this nature.