Hi, I'm Sreeram! I'm a current high school student incoming to the University of Texas at Austin for Computational Engineering at the Cockrell School of Engineering and the Oden Institute for Computational Engineering and Sciences. My work focuses on numerical methods for differential equations, specifically spatial discretization, time integration, and linear solvers across computational science and engineering domains I was awarded a full Cockrell Engineering Honors Scholarship and intend to advance research in computational mathematics, science, and engineering through the Oden Institute and the ASE/EM Department
Research questions that I've previously and currently exploring, focusing on the interaction and effects of numerical methods in various types and scenarios. My work is currently under Jesse Chan at the University of Texas at Austin's Oden Institute for Computational Engineering and Sciences.
Developing a framework for nonlinear fully discrete stability analysis of hyperbolic PDE solvers, motivated by modified Patankar–Runge–Kutta methods that enforce positivity. The work extends classical von Neumann analysis toward state-dependent spectral behavior tracking, with the goal of analyzing how finite volume discretizations and positivity-preserving time integration interact in nonlinear settings.
Studying the spectral behavior of isogeometric analysis relative to standard finite element methods, with emphasis on how discretization structure influences eigenvalue distributions and numerical performance. Current and planned directions include extending this comparison into nonlinear structural dynamics to understand how geometric smoothness, basis continuity, and nonlinearity affect the evolving spectrum of IGA versus FEM.
A collection of scientific and numerical projects that I've worked on, excluding research and contributions, focusing on developing numerical methods and software for solving scientific problems.
A Julia-based numerical laboratory for studying geometric multigrid cycle behavior, smoother performance, residual decay, and FFT-resolved spectral effects in 2D finite-difference Poisson problems.
A controlled numerical framework for SSA, CLE, and solver comparison, built to study how modeling, discretization, and randomness architecture shape stochastic chemical dynamics.
Open source contributions to numerical and scientific projects and packages that I've worked on, including code, documentation, and issue tracking.
Focuses and skills across computational mathematics and science that I've worked with or am currently exploring in my research, projects, and contributions