High-Order Positivity Preserving Methods for Conservation Laws Research Advisor: Professor Chi-Wang Shu

• Designed positivity-preserving post-processing for nonlinear pressure function in the Euler equations
• Prevented numerical blow-ups, ill-posedness, and non-physical distortions of numerical solutions
• Implemented challenging test cases in MATLAB and Fortran using MPI on Brown’s HPC cluster
• Demonstrated algorithm’s numerical accuracy, robustness, simplicity, and versatility for CFD applications
• Manuscript published in Research in the Mathematical Sciences (see Publications)

Positivity Preserving Implicit Continuous Galerkin Framework Research Advisor: Dr. Eirik Endeve

• Extended positivity-preserving post-processing for implicit continuous finite element method
• Designed novel correction procedure for large magnitude negative density and pressure violations
• Developed multigrid acceleration protocol to speed up convergence for high quantity errors
• Implemented challenging test cases in FEniCS with PETSc for nonlinear Newton solver
• Manuscript submitted to Communications on Applied Mathematics and Computation (see Publications)

Robustness Metrics for Tumor Volume Delineation CNN Research Advisor: Professor Martin Frank

• Measured robustness of deep learning model for automated head and neck tumor volume delineation.
• Augmented computer tomography data with MONAI and ran inference on nnU-Net model with PyTorch.
• Produced Jupyter Notebooks with robustness tests easily extendable to different augmentation methods.
• Found model was not robust to significant augmentations, delivered report, and presented findings.

Optimal Coefficients of Runge Kutta Schemes with Machine Learning Research Advisor: Professor Martin Frank

• Created numerical schemes for ordinary differential equations using artificial neural networks.
• Found optimal coefficients of Runge Kutta schemes with a target order of accuracy.
• Produced new methods, rediscovered classical schemes, and reduced computation cost for stiff problems.
• Constructed neural networks using TensorFlow and the Keras deep learning API in Python.

Implicit High-Order Operator Splitting Schemes Research Advisors: Dr. Cory Hauck and Dr. Zachary Grant

• Developed implicit high-order operator splitting schemes for stiff differential equations.
• Produced MATLAB codes in Computer Science & Mathematics Division.
• Delivered an abstract, poster, and report paper to the Department of Energy.
• Implemented novel correction method to reduce computation cost for stiff problems.

NSF Graduate Research Fellow ; GEM Fellow

• Advisor: Prof. Chi-Wang Shu
• Research: High-order positivity-preserving numerical methods for Euler equations, WENO schemes, and computational fluid dynamics (CFD).
• Expected Graduation: May 2027

• Focus on Numerical Analysis, Scientific Computing, and Fluid Dynamics.

• GPA: 4.0/4.0 (Elford C. Morgan Award for Highest Academic Standing)
• Research: Graph theory for DNA nanostructure assembly and mechanistic epidemiological modeling (COVID-19).