Research

Areas

• Numerical methods and analysis for PDE
• Diffuse domain methods and transmission-type boundary conditions
• Multigrid methods and fast solvers
• Mathematical imaging and computational geometry
• Scientific machine learning (GNN + reinforcement learning)

Selected Publications

Book

• S. M. Wise, A. J. Salgado, and M. H. Wong, Multigrid Methods: Axiomatic Convergence Theory for Linear and Weakly Nonlinear Problems, De Gruyter, 2025. ISBN: 978-3-11-135488-0. Publisher page

Preprints

• T. Luong, T. Mengesha, K. Stinson, S. M. Wise, and M. H. Wong, The α-Limit Problem: Convergence of a Linear Degenerate Interface Transmission Problem, arXiv:2609.01237 [math.AP], 2026. arXiv
• M. H. Wong, The symmetric V-cycle can diverge under the multigrid axioms for cell-centred discretisations, arXiv:2607.23391 [math.NA], 2026. arXiv

Journal Articles

1. T. Luong, T. Mengesha, S. M. Wise, and M. H. Wong, A Diffuse Domain Approximation with Transmission-Type Boundary Conditions II: Gamma-Convergence, International Journal of Numerical Analysis and Modeling, 22(5):728-744, 2025. DOI
2. T. Luong, T. Mengesha, S. M. Wise, and M. H. Wong, A Diffuse Domain Approximation with Transmission-Type Boundary Conditions I: Asymptotic Analysis and Numerics, International Journal of Numerical Analysis and Modeling, 22(5):694-727, 2025. DOI
3. M.-H. Wong, M. Li, K.-M. Tam, H.-M. Yuen, C.-T. Au, K. C.-C. Chan, A. M. Li, and L.-M. Lui, A Quasiconformal-Based Geometric Model for Craniofacial Analysis and Its Application, Axioms, 12(4):393, 2023. DOI

Invited and Conference Talks

• SIAM SEAS 2025 (Invited Talk): “Gamma-Convergence and Asymptotic Analysis for a Diffuse Domain Problem with Transmission Boundary Conditions: Part 2, Numerical Confirmation”
• UARK-SIAM-CSS 2025 Conference (Invited Talk), University of Arkansas, Fayetteville, AR: “Gamma-Convergence and Asymptotic Analysis for a Diffuse Domain Problem with Transmission Boundary Conditions: Part 2, Numerical Confirmation”
• Workshop on Theoretical and Numerical Challenges in Materials Science (2024), University of Alabama
• UROP Workshop (2022), CUHK: “Preliminary Diagnosis of Childhood Obstructive Sleep Apnea using 2D Images by Quasi-Conformal Geometry”

Current and Recent Projects

• Diffuse Domain Methods for Poisson PDE
  • Asymptotic behavior, numerics, and Gamma-convergence analysis
  • Co-supervised by Steven M. Wise and Tadele Mengesha
• Combinatorial Optimization with GCN + Deep RL
  • ORNL + UTK collaboration
  • Optimization workflow design for scientific applications
• Medical Imaging for Early Diagnosis of Childhood Obstructive Sleep Apnea
  • Quasiconformal-geometry-based craniofacial analysis from 2D images
  • Classification workflow development for early-stage diagnosis

Selected Awards

• Spike Tickle STEM Endowed Fellowship (UTK, 2026)
• Dawn and Lawrence Taylor Graduate Fellowship (UTK, 2025)
• Dorothea and Edgar D. Eaves Graduate Student Teaching Award - Senior (UTK, 2025)
• Department of Mathematics Fellowship (UTK, 2022)
• Undergraduate Research Opportunities Programme (UROP) Gold Award (CUHK, 2022)
• Chung Chi College Kunkle and Pommerenke Full Tuition Scholarship (CUHK)
• Chung Chi College Departmental Prize - Enrichment Mathematics (CUHK, 2022)
• Chung Chi College Scholarship for Excellence (CUHK, 2021)
• Faculty of Science Dean’s List (CUHK, five-time awardee)
• Undergraduate Mathematics Scholarship, Department of Mathematics (CUHK, five-time awardee)