My current research focuses on the design and analysis of accurate multiscale discretization techniques for solving partial differential equations (PDEs). This includes modeling multiphysics systems such as fluid-poroelastic interactions and developing effective cell-centered discretizations for linear elasticity. I also develop parallel scientific software for large-scale simulations of fluid flow through porous media, with experience in C++, MPI/OpenMP, deal.II, Git, Slurm, and research software engineering. Previously, I worked on topics in analytical PDEs, mainly infinity harmonic functions and convex integration.
I also have experience with data-driven modeling, machine learning, optimization, and statistical computing. I participated in the IMA Math-to-Industry Boot Camp XI at the University of Minnesota and the 2024 Mathematical Problems in Industry Workshop, and have attended research software and HPC workshops, including through URSSI and the Pittsburgh Supercomputing Center. Through these programs and projects, I have worked with Python and R based tools for regression, classification, clustering, neural networks, PCA/SVD, and mathematical optimization. I have also applied these skills in an industry-facing project with Vironix Health, where our team used data cleaning, visualization, regression, clustering, Gaussian process regression, PCA, and neural-network models to analyze patient health outcomes and chronic kidney disease progression.
Publications:
Manraj Ghumman, Manu Jayadharan, Ivan Yotov, Domain decomposition methods for the Stokes-Biot model of fluid-poroelastic structure interaction, submitted. https://doi.org/10.48550/arXiv.2606.17363
Manraj Ghumman, Jan M. Nordbotten, Boris Tzankov, Ivan Yotov, Expanded mixed finite element methods for elasticity, in preparation.
Selected Reports :
Analyzing the Influence of Virtual Care Management on Patient Health Outcomes and Risk Stratifying Chronic Kidney Disease Patients for Stage Degeneration. Mathematics in Industry Reports (MIIR), SIAM Mathematical Problems in Industry Workshop.
A numerical and stochastic approach for modeling cell population dynamics in colonic crypts undergoing asymmetric cell divisions. Graduate Student Mathematical Modelling Camp (GSMMC) by SIAM.
Master's Thesis : Lipschitz Extension Problem.
Lipschitz Extension Problem (Masters Thesis Defence), IISER Pune, June 2021.
Infinity Harmonic Functions and Calculus of Variations, Analysis and Geometry Seminar, Math Department IIT Gandhinagar, Jan 2022.
You can find a brief description of my past projects in my CV.