Research

My work develops computational methods for partial differential equations, with an emphasis on preserving mathematical structure while making large-scale models practical to solve.

Research

Low-Rank Stochastic Navier–Stokes Solvers

Low-rank tensor-decomposition-based solvers for time-dependent Navier–Stokes equations with stochastic viscosity.

Observability-Preserving Discretizations

Numerical discretizations that preserve the boundary observability and control properties of continuous beam models by addressing spurious high-frequency modes introduced by standard methods.

Piezoelectric Beam Stabilization

Boundary-feedback design for fast suppression of coupled mechanical and electromagnetic vibrations.

SoTL

Scholarship of Teaching and Learning in Mathematics

Developing symbol sense, conceptual understanding, and productive comfort with ambiguity in mathematics.

Wolfram Demonstrations

Vibration Suppression on a Hinged Three-Layer Sandwich Beam

Interactive boundary control of a layered sandwich beam with filtering and vibration suppression.

Feedback Sensor Design for a Cantilevered Three-Layer Sandwich Beam

A visual sensor-design experiment for a layered beam clamped at one end and free at the other.

Stabilization of the Wave Equation by Direct Fourier Filtering

A boundary-controlled wave-equation model comparing direct Fourier filtering with an order-reduced discretization.

Boundary-Feedback Control of Vibrations on a String with and without Filtering

An interactive comparison of boundary damping, filtering, and order-reduced numerical models for a vibrating string.

Dynamics of a Longitudinal Piezoelectric Beam

An interactive view of coupled mechanical motion, electrical response, sensing, and actuation.

Stabilization of a Smart Beam with a Tip Mass

An interactive observer-controller model for a magnetizable piezoelectric beam with a dynamic tip load.

Rapid Stabilization of Heat and Structure Interactions with Boundary Feedback Controllers

An interactive heat-structure model showing how thermal and mechanical dynamics can be stabilized together.