PhD student in Mathematics

Calvin Wong

I am a PhD student in Mathematics at the University of Tennessee, Knoxville, expecting to graduate in 2027. My interests span applied mathematics, scientific machine learning, and agentic coding, with current work on numerical PDEs, multigrid methods, and learning-based optimization.

Research View CV

Research

Research interests

Research overview

Diffuse domain methods

Solving PDEs on complicated geometries without regridding. I study Poisson problems with transmission-type boundary conditions.

Multigrid methods

I study convergence theory and implement efficient multigrid solvers for PDEs.

Scientific machine learning

Graph convolutional networks and deep reinforcement learning for combinatorial optimization.

Other research interests include finite difference and finite element analysis, mathematical imaging, differential geometry, and quasiconformal methods.

Current focus

Block-structured adaptive multigrid

BSAM in MATLAB provides solvers for two-dimensional elliptic, parabolic, and diffuse-domain problems, with refinement concentrated where the solution or geometry needs it.

BSAM in MATLAB

BSAM starfish transmission example: diffuse-domain solution surface and five-level adaptive mesh around the interface — Starfish transmission problem: solution and adaptive mesh · View full figure

Five levels of the actual BSAM patch hierarchy, from spacing 4/64 to 4/1024, with a close-up of cell edges near the starfish tip — Grid hierarchy and cell-level close-up · View full figure

Relative algebraic residual decreases over ten V-cycles; adjacent plot shows the adaptive solution minus a uniform 1024-squared numerical reference at fixed interface width — Algebraic residual reduction and comparison with a uniform numerical reference · View full figure

Publications

Book and recent preprints

All publications

Cover of Multigrid Methods by Wise, Salgado, and Wong — De Gruyter · 2025

Book · 2025

Multigrid Methods: Axiomatic Convergence Theory for Linear and Weakly Nonlinear Problems

S. M. Wise, A. J. Salgado, and M. H. Wong

De Gruyter · ISBN 978-3-11-135488-0

Publisher

Figure 8.1: limiting solution and finite-difference solutions for alpha 0.2, 0.5, and 0.8, with a zoom near the interface — α-limit preprint · Fig. 8.1

Preprint · 2026

The α-Limit Problem: Convergence of a Linear Degenerate Interface Transmission Problem

T. Luong, T. Mengesha, K. Stinson, S. M. Wise, and M. H. Wong

arXiv:2609.01237 [math.AP]

arXiv

Figure 5.4: V-cycle iterates depart from the manufactured solution while W-cycle iterates approach it in the plotted example — V-cycle preprint · Fig. 5.4

Preprint · 2026

The symmetric V-cycle can diverge under the multigrid axioms for cell-centred discretisations

M. H. Wong

arXiv:2607.23391 [math.NA]

arXiv

Internships

Oak Ridge National Laboratory

I served as a Summer Internship Scientist at Oak Ridge National Laboratory in the summers of 2024, 2025, and 2026. My work there involved computational optimization and machine learning for scientific applications.

Teaching & projects

Teaching and software

I teach mathematics at UT Knoxville and develop software for teaching and LaTeX writing.

Teaching Projects Agentic Coding

AI-assisted LaTeX editing

TexMacgic

A macOS LaTeX editor with agent integrations for Codex, Claude Code, and Antigravity.

Agent tools in TexMacgic