Advanced Models and Scalable Computational Frameworks for Complex Systems

Research Overview

My work sits at the interface of applied mathematics, computational science, and engineering, with a focus on designing rigorous mathematical formulations, high-order numerical methods, and efficient computational solvers for complex multiphysics systems governed by nonlinear partial differential equations. By integrating stability analysis, multiscale modeling, inverse methods, and data-driven computation, I translate mathematical theory into robust tools that enable predictive simulation, optimization, and engineering innovation.

A defining objective of my research is to develop generalizable algorithms and software frameworks that remain valid across a wide range of application domains. As a result, my studies naturally support and connect to challenges in mechanical engineering, aerospace engineering, biomedical engineering, civil engineering, energy and industrial engineering, materials engineering, computational engineering, as well as medicine and biology.

Core Research Thrusts

Methodologically, my research emphasizes robust computational solvers and analysis tools, including finite element methods, discontinuous Galerkin methods, finite volume methods, spectral methods, ENO/WENO high-order schemes, boundary element methods, and ALE moving-mesh methods. I also develop efficient numerical solvers for complex differential systems and favor analytical solutions to simplified problems whenever possible to guide computation and strengthen physical interpretation.

Selected Research Directions and Impact

Inverse Problems and Medical Imaging: Wavelet-Based MIT Reconstruction

I am developing wavelet-based algorithms for high-resolution image reconstruction in magnetic induction tomography (MIT), a noninvasive and noncontact approach for electrical conductivity imaging. Because conductivity differs with disease, MIT holds promise for accessible diagnostic imaging. My work focuses on single-coil MIT image reconstruction, including mesh-free methods that reduce reliance on precisely known target boundaries. The approach discretizes the convolution integral using wavelets to automatically place spatial resolution where needed, and employs regularized least squares and advanced linear algebra (including SVD) to stabilize underdetermined reconstructions. The long-term goal is an efficient meshless algorithm that could be implemented on a portable device (e.g., tablet-class hardware), enabling low-cost imaging—particularly in remote and underserved communities—while also supporting industrial imaging and computational electromagnetics.

This direction benefits interdisciplinary research communities in computer science, engineering, mathematics, and medical physics, and supports industrial development in imaging, medical devices, computational electromagnetics, GPU-accelerated linear algebra, and uncertainty quantification through error estimation.

---

Thin Swelling Porous Media and Multilayer Unsaturated Transport

Porous media are ubiquitous across nature and engineering, from groundwater flow and oil recovery to diffusion in biological tissue scaffolds and industrial curing. A major focus of my work is modeling unsaturated flow through multiple layers of thin, swelling porous media—a multiscale problem in which pore-scale physics influences macroscale behavior. Using rigorous multiscale modeling and numerical analysis, I develop transport models that capture deformation, storage, and inter-layer exchange, enabling predictive simulations for filtration, energy systems, medical devices, and absorbent materials (e.g., wipes, paper towels, feminine pads, and diapers).

---

Industrial Collaboration: Kimberly-Clark Modeling of Thin Absorbent Porous Structures

In collaboration with Kimberly-Clark, I contributed to modeling wicking and partially saturated flow in multilayer thin swelling porous media. I am among the few researchers applying the volume-averaging technique—a rigorous upscaling approach—to develop efficient macroscopic models for these systems. The resulting model supports fast, accurate, and cost-effective simulation workflows and is used to help predict and understand fluid flow and deformation processes in thin porous media relevant to product design (including diaper performance). This work accelerates product development by reducing experimental iteration time and providing physically grounded predictive capability.

Using similar volume-averaging ideas, I also developed macroscopic modeling approaches relevant to water management in polymer electrolyte membrane fuel cells (PEMFCs), where transport in porous layers is a key limitation for high performance. More broadly, this framework extends naturally to porous-media problems across geology, chemical reactors, drying and liquid composite molding, combustion, and biomedical systems such as tissue scaffolds, brain tissue transport, macromolecule transport, and thermal simulations in biological tissues.

---

Fluid Mechanics: Stability, Turbulence, Free-Surface Flow, and Engineering Applications

My Ph.D. work at Virginia Tech centered on the stability of parallel shear flows—one of the foundational problems in fluid mechanics—with emphasis on viscoelastic flows and transition mechanisms. Subsequently, my research at the University of Maryland focused on hydrodynamic stability of multiphase flows, including perturbation analysis of interfacial instability and high-order numerical methods for quantifying nonlinear evolution of unstable structures in microchannel configurations. I also contributed to studies in free-surface turbulent flows using anisotropic algebraic Reynolds stress modeling to predict the hydrodynamic response of open channels with heterogeneous bed roughness, including improved closure models for wall friction and momentum dispersion.

Beyond stability, my work includes computational engineering projects such as numerical simulation and control of unmanned underwater vehicles (UUVs), addressing applications including seabed exploration, pollutant tracking, offshore industry support, and underwater inspection.

Methods, Computation, and Generalizable Tool-Building

I develop efficient numerical solvers for complex systems of differential equations using high-order computational methods and scientific computing practices. My work spans inverse problems, data science and visualization, machine learning, computational biology (including cardiovascular modeling), multiphase flow in porous media, and nonlinear dynamics in PDEs/ODEs (including chaos, optimal control, and dynamical systems). Recent efforts expand toward inverse problems and machine learning for biomedical applications, while maintaining broad relevance across engineering and scientific computing.

• Numerical PDE methods: FEM, DG, FVM, spectral methods, ENO/WENO, BEM, ALE
• Scientific computing: scalable solvers, high-performance simulation, parallel computing
• Mathematical analysis: stability theory, perturbation methods, asymptotics, spectral analysis
• Data-driven methods: inverse modeling, regularization, ML/AI for scientific computing

Funding and Collaboration Vision

I am actively developing competitive research proposals and expanding interdisciplinary collaborations to build a sustainable, externally funded research program. Current and planned proposals target major federal agencies and industry partnerships, including:

• National Science Foundation (NSF)
• Department of Energy (DOE)
• National Institutes of Health (NIH)
• Department of Defense (DoD)
• Industry partnerships

These efforts focus on advancing mathematical modeling, scientific computing, multiscale simulation, inverse problems and imaging, and AI/ML-enhanced computational methods, with broad applicability across engineering fields, medicine, and biological systems.