Research Overview
My research lies at the intersection of applied mathematics, computational science, and engineering, with emphasis on mathematical modeling and numerical simulation of systems governed by nonlinear partial differential equations. I develop analytical and computational methods that translate mathematical theory into reliable predictive tools applicable across engineering, physics, and biomedical sciences.
This work integrates stability theory, multiscale modeling, inverse problems, and high-performance scientific computing to address challenges involving transport phenomena, fluid mechanics, imaging, and multiphysics systems. The ultimate goal is to design generalizable mathematical and computational frameworks capable of solving real-world scientific and engineering problems.
Core Research Areas
High Performance Scientific Computing and Numerical Methods
Development of high-order finite element, finite volume, and spectral methods for solving complex systems of differential equations.
Computational Medicine & Biomedical Simulation.
I develop advanced mathematical models, high-performance simulation, and AI-driven inverse methods to analyze physiological systems, medical imaging, and disease mechanisms—supporting next-generation healthcare technologies and precision medicine.
- Biomedical modeling & simulation for cardiovascular systems, tissue transport, and medical imaging
- Medical imaging & inverse modeling (regularized reconstruction, wavelets, meshless discretization)
- Computational biomedicine integrating mechanistic models with data-driven inference
- Scientific software development and simulation frameworks
Fluid Mechanics and Hydrodynamic Stability
Mathematical and computational analysis of flow stability, turbulence transition, and multiphase flow dynamics.
Porous Media and Multiscale Transport
Modeling of flow, deformation, and transport in porous structures using rigorous multiscale mathematical frameworks.
Inverse Problems and Scientific Imaging
Development of mathematical and computational methods for image reconstruction, parameter estimation, and inverse modeling.
Selected Research Contributions
My research includes wavelet-based computational imaging methods for magnetic induction tomography, enabling improved reconstruction accuracy in inverse imaging systems.
I have developed mathematical models for thin swelling porous media and multiscale transport phenomena, providing predictive simulation capability for engineering and industrial systems.
My work in fluid mechanics includes theoretical and computational studies of hydrodynamic stability, multiphase flow, and nonlinear flow dynamics.
Computational and Mathematical Methods
- Finite element, finite volume, and spectral methods
- High-performance and parallel scientific computing
- Stability analysis and perturbation theory
- Inverse modeling and parameter estimation
- Scientific software development and simulation frameworks