Yue Wu (吴越) Ph.D. Candidate E-mail: Yue_Wu3 [at] Brown [dot] 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 main research interests include numerical analysis and scientific computing. He grew up in Wuxi, a beautiful city in eastern China. Outside academia, he is an aviation enthusiast and 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, RI 02912, USA
  Advisor: Prof. Chi-Wang Shu
• 09/2023 – 05/2025: M.Sc. in Applied Mathematics
  Division of Applied Mathematics, Brown University, 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

• High-order numerical methods for partial differential equations
  • Discontinuous Galerkin finite element methods
  • Finite difference weighted essentially non-oscillatory (WENO) methods
• Scientific computing
  • Parallel PDE solver development

Publications and Preprints

1. 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 (2025), pp. 373–422. doi: 10.4310/BPAM.250415002006.
2. 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 (2025), Paper No. 114104, 24 pp. doi: 10.1016/j.jcp.2025.114104. MR4912873.

Research Experiences

• Efficient alternative WENO (A-WENO) methods for compressible Euler equations
  Brown University; Supervisor: Prof. Chi-Wang Shu; 09/2024 – 02/2025
  • Investigated the effect of different transform variables in the local characteristic decomposition on the performance of A-WENO methods.
  • Developed an A-WENO code using Riemann invariants as transform variables to save cost.


• Discontinuous Galerkin Methods for the p-Laplace Equation
  Bachelor's Thesis at USTC; Supervisor: Prof. Yan Xu; 12/2022 – 06/2023
  • Proved an a priori error estimate for an LDG scheme for the p-Laplace equation.
  • Developed and implemented 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.


• Positivity-Preserving Conservative Low-Rank Methods for Vlasov Dynamics
  Purdue University (remote); Supervisor: Prof. Xiangxiong Zhang; 06/2022 – 08/2022
  
  • Developed a low-rank correction algorithm with positivity preservation and orthogonality constraints via optimization, which can post-process data from a dynamic low-rank solver.
  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.


• 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.
  • Checked 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 Experiences

• Fall 2025 at Brown: Teaching Assistant, APMA 0160 - Introduction to Scientific Computing (Instructor: Dr. Rami Masri).
• Spring 2025 at Brown: Teaching Assistant, APMA 1650 - Statistical Inference I (Instructor: Prof. Sarah Brauner).
• Fall 2024 at Brown: Teaching Assistant, APMA 1210 - Operations Research: Deterministic Models (Instructor: Prof. Amalia V. Culiuc)
• Spring 2022 at USTC: Teaching Assistant, Computational Methods B (Instructor: Prof. Jingrun Chen)

Professional Services

• Reviewer for Journal of Computational Physics and Journal of Scientific Computing since 2025

Professional Skills

• Programming: MATLAB, C++, Fortran, Python, MPI, OpenMP
• Software: LaTeX, Mathematica, NGSolve, FEniCS, MFEM
• Language: Mandarin Chinese, English

Honors and Awards

• 06/2024: New Lotus Award, SGY Rose Scholarship 2023
• 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, 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