Yue Wu (吴越) Ph.D. Candidate E-mail: yue_wu3@brown.edu Yue Wu is a Ph.D. candidate in the Division of Applied Mathematics at Brown University under the supervision of Prof. Chi-Wang Shu. His research focuses on high-order numerical methods for PDEs, particularly discontinuous Galerkin methods, structure-preserving discretizations, and robust algorithms for nonlinear PDEs. He grew up in Wuxi, a beautiful city in eastern China. Outside academia, he enjoys road cycling, hiking, and road trips. Please find his CV here.

Education

• 09/2023 – present: Ph.D. Candidate
  Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
  Advisor: Prof. Chi-Wang Shu
• 09/2023 – 05/2025: M.Sc. in Applied Mathematics
  Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
  GPA: 4.0/4.0
• 09/2019 – 06/2023: B.Sc. in Information & Computational Science
  School of the Gifted Young (SGY), University of Science and Technology of China (USTC), Hefei, Anhui 230026, China
  GPA: 3.96/4.3 (Ranked 1st in major)
• 09/2017 – 06/2019: Wuxi No. 1 High School, Wuxi, Jiangsu 214031, China

Research Interests

• Numerical methods for partial differential equations (PDE)
  • Discontinuous Galerkin (DG), finite element, and spectral element methods
  • Finite difference Weighted Essentially Non-Oscillatory (WENO) methods
  • Structure-preserving numerical methods
• Scientific computing
  • Low rank methods
  • PDE-constrained optimization
  • Parallel PDE solver development
  • Tool-augmented and automated computational research workflows

Publications and Preprints

1. Y. Wu and C.-W. Shu. Unconditionally $L^2$-stable explicit--implicit--null filtered Runge--Kutta methods for general nonlinear degenerate parabolic equations. Submitted to Numer. Math. arXiv:2611.02282.
2. Y. Wu and C.-W. Shu. Energy stability of explicit--implicit--null time discretizations for a class of nonlinear degenerate parabolic equations with state-dependent coefficients. Submitted to ESAIM: M2AN arXiv:2610.34539.
3. Y. Wu, S. Becker, J.-M. Qiu, and X. Zhang. Nonnegative low-rank matrix correction under an orthogonality constraint in conservative Vlasov simulations. Submitted to J. Sci. Comput. arXiv:2607.26272.
4. Y. Wu and C.-W. Shu. A positivity preserving and entropy stable nodal discontinuous Galerkin scheme for ideal MHD. Submitted to Commun. Math. Stat. arXiv:2604.23885.
5. Y. Wu and C.-W. Shu. Finite difference alternative WENO schemes with Riemann invariant-based local characteristic decompositions for compressible Euler equations. J. Comput. Phys., 537:114104, Sept 2025. doi: 10.1016/j.jcp.2025.114104. MR4912873. arXiv:2502.08043.
6. Y. Wu and Y. Xu. A high-order local discontinuous Galerkin method for the $p$-Laplace equation, Beijing J. of Pure and Appl. Math., 2(1):373–422, Apr 2025. doi: 10.4310/BPAM.250415002006. arXiv:2311.09119.

Research Experience

1. Novel bound-preserving discontinuous Galerkin methods for conservation laws
   Collaborator: Prof. Zheng Sun, 11/2026 till now


2. Explicit--Implicit--Null (EIN) Time Stepping for Nonlinear Degenerate Parabolic Equations
   Brown University, Supervisor: Prof. Chi-Wang Shu, 10/2026
   • Proved unconditional energy stability of EIN methods for nonlinear diffusion with gradient flow structure.
   • Developed novel unconditionally $L^2$-stable EIN filtered Runge--Kutta for general nonlinear diffusion.


3. Structure-Preserving Discontinuous Galerkin Schemes for Magnetohydrodynamics (MHD)
   Brown University, Supervisor: Prof. Chi-Wang Shu, 03/2025 – 04/2026
   • Investigated all types of time-explicit structure-preserving conservative schemes for ideal MHD.
   • Developed a nodal discontinuous Galerkin scheme that combines positivity preservation and entropy stability for the first time in literature.


4. Efficient A-WENO Methods for Compressible Euler Equations
   Brown University, Supervisor: Prof. Chi-Wang Shu, 09/2024 – 02/2025
   • Investigated the effect of transform variables in local characteristic decompositions on A-WENO performance and proved the optimal practice.
   • Implemented A-WENO methods using a carefully selected set of Riemann invariants to reduce computational cost.


5. Discontinuous Galerkin Methods for the $p$-Laplace Equation
   Bachelor's Thesis at USTC, Supervisor: Prof. Yan Xu, 12/2022 – 06/2023
   • Proved rigorous a priori error estimates for a high order local DG scheme.
   • Developed an efficient preconditioned gradient descent method.
   Abstract

   We study the high-order local discontinuous Galerkin (LDG) method for the p-Laplace equation. We reformulate our spatial discretization as an equivalent convex minimization problem and use a preconditioned gradient descent method as the nonlinear solver. For the first time, a weighted preconditioner that provides hk-independent convergence is applied in the LDG setting. For polynomial order k ≥ 1, we rigorously establish the solvability of our scheme and provide a priori error estimates in a mesh-dependent energy norm. Our error estimates are under a different and non-equivalent distance from existing LDG results. For arbitrarily high-order polynomials under the assumption that the exact solution has enough regularity, the error estimates demonstrate the potential for high-order accuracy. Our numerical results exhibit the desired convergence speed facilitated by the preconditioner, and we observe best convergence rates in gradient variables in alignment with linear LDG, and optimal rates in the primal variable when 1 < p ≤ 2.


6. Positivity-Preserving Conservative Low Rank Methods for Vlasov Dynamics
   Purdue University (remote), Supervisor: Prof. Xiangxiong Zhang, 06/2022 – 08/2022
   
   • Developed multiple nonnegative low rank correction algorithm under orthogonality constraints using convex optimization and tangent space accelerated projection.
   • Incorporate the algorithm into the dynamic low rank Vlasov solver as a positivity preserving conservative limiter to obtain robust and physically meaningful simulation.
   Abstract

   The high-dimensionality of Vlasov dynamics makes it expensive to solve by traditional numerical methods. Utilizing the low-rank structure of the solution, people have developed cost-efficient methods using low-rank matrix/tensor approximation. However, very often a low-rank approximation of a given non-negative matrix (which corresponds to the solution) can have negative elements which results in non-physical solutions. In this research, our goal is to develop a cost-efficient positivity-preserving conservative low-rank method to solve this problem. We designed two algorithms, one is the tangent-space accelerated alternating projection algorithm, and the other is the nuclear norm optimization, both with macroscopic quantities conservation.


7. Numerical Simulation of Plasma Equilibrium Evolution in Nuclear Fusion
   USTC undergraduate research project, Supervisor: Prof. Mengping Zhang, 06/2021 – 05/2022
   
   • Developed a parallel hybrid finite difference-pseudo spectral code for resistive MHD in toroidal geometry, and performed long-time simulation of resistive tearing mode instability in tokamaks.
   • Validated the results with researchers from the Institute of Plasma Physics, CAS, and against those from existing open-source codes.
   • Research report (in Chinese) preview: here; Defense slides (in Chinese) preview: here.
   Abstract

   The controlled nuclear fusion is one of the most prospective solution to the energy crisis and environmental problems. The tokamak has been widely investigated as the most feasible magnetically confined fusion device. Tearing mode instabilities have great influence on the fusion reaction thus worth studying. In this research, in order to simulate the evolution process of tokamak plasma equilibrium numerically, we review different formulations of the MHD equations, select a suitable type of non-conservative resistive MHD that is based on perturbation variables, and develop a parallel program using hybrid finite difference-Fourier pseudo spectral method in cylindrical coordinates. Using our program, we simulate the (m,n)=(2,1) resistive tearing mode instability and compare the results against those obtained from the CLT and M3D-C1 code. The results show that our program exhibits satisfactory performance in conserving numerical divergence of the magnetic field, fitting the theoretical relation between logarithmic growth rate of kinetic energy and resistivity, revealing the mode structure independent of initial perturbation at the linear stage and reaching the final saturation stage.

Teaching Experience

1. TA at Brown, Fall 2026: APMA 0355 – Applied Ordinary Differential Equations with Theory (Instructor: Dr. Kristina Mallory)
2. TA at Brown, Spring 2026: APMA 1655 – Introduction to Probability and Statistics with Theory (Instructor: Prof. Hui Wang).
3. TA at Brown, Fall 2025: APMA 0160 – Introduction to Scientific Computing (Instructor: Dr. Rami Masri).
4. TA at Brown, Spring 2025: APMA 1650 – Statistical Inference I (Instructor: Prof. Sarah Brauner).
5. TA at Brown, Fall 2024: APMA 1210 – Operations Research: Deterministic Models (Instructor: Prof. Amalia V. Culiuc)
6. TA at USTC, Spring 2022: Computational Methods B (Instructor: Prof. Jingrun Chen)

Professional Service

• Journal reviewer for J. Comput. Phys. and J. Sci. Comput. (since 2025), and Comput. Math. Appl. (since 2026)

Professional Skills

• Programming: C++, MATLAB, Python, Fortran 2008, MPI, OpenMP
• Software: NGSolve, FEniCS, MFEM, Mathematica, Keras, Tecplot
• Tools: Linux, Git, Jupyter, LaTeX, Markdown
• Language: Mandarin Chinese, English

Honors and Awards

• 06/2023: USTC Outstanding Undergraduate Award
• 06/2023: "Chia-Chiao Lin" Gold Medal in Applied and Computational Math track (Top 1 in China) & Team Silver Medal & Excellence Prize in Analysis and PDEs track, the 14th S.-T. Yau College Student Math Contest
• 10/2022: Gold Prize, USTC Outstanding Student Scholarship
• 08/2022: Excellence Prize in Analysis and PDEs track, the 13th S.-T. Yau College Student Math Contest
• 12/2021: China National Scholarship
• 12/2021: Second Prize, the 13th Chinese Math Competitions
• 12/2020: China National Scholarship
• 09/2019: Third Prize, USTC Freshman Scholarship

Posters and Presentations

• 07/2024: Poster session, the 2024 International Congress of Basic Science (ICBS), Beijing, China

Contact Information

ORCID: 0009-0006-3898-8204
GitHub: YueWu2002
Other links: ResearchGate, arXiv, Google Scholar, Web of Science, LinkedIn

Miscellaneous

• 中国科大 数学分析B2 课程笔记（含作业题和历年期末试题解答） 文件
• 中国科大 微分方程I（现微分方程引论）课程笔记 文件
• 中国科大 有限元方法 课程作业 HW1 (一维线性单元)， HW2 (一维二次单元)， HW3 (一维纯Neumann边界)， HW4 (二维线性单元)， HW5 (二维二次单元)
• 有限差分 WENO 方法笔记 文件
• 布朗大学 APMA2560 偏微分方程数值解 II 大作业 文件
• 理想气体可压 Euler 方程精确黎曼求解器（支持真空） matlab 代码
• 可压 Euler 方程组 HLL/HLLC 数值通量优化实现 matlab 代码
• Counter examples in numerical methods for PDEs:
  • Globally divergence-free discontinuous Galerkin methods for ideal compressible MHD equations is not positivity-preserving in the lowest-degree case in some sense. example
  • Cell averages of discontinuous Galerkin solutions of a simple linear scalar constant-coefficient advection equation with P1 or Q1 polynomials on 2D Cartesian grids using backward Euler time stepping are not bound-preserving! example