In my spare time, I enjoy playing tennis and making music. I play the violin, the cello and an ancient chinese instrument called the guqin (all at a very amateur level).

I also have an interest for languages. I am fluent in English, French, and Chinese and I have taken 5 semesters of German courses. I like the sound of different languages and would like to learn a couple more if I had the time.

Education

  • Doctor of Philosophy 2016-2021
    Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada
    Supervisor: Prof. Jean-Christophe Nave
    Thesis: Characteristic Mapping Framework with Applications to Density Transport and Fluid Dynamics [pdf]
  • Master of Science 2015-2016
    Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada
    Supervisor: Prof. Jean-Christophe Nave
    Co-supervisor: Linan Chen
    Thesis: Characteristics Mapping Methods and Application to Adaptive Moving Mesh [pdf]
  • Bachelor of Science 2012-2015
    Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada

Training

  • Summer School 200 years of Navier-Stokes and Turbulence
    École de Physique les Houches
    August 2023
  • Workshop on Numerical Analysis of Singularly Perturbed PDEs
    AARMS, Saint Mary's University, Halifax
    July 2016
  • Workshop on Domain Decomposition Methods for PDEs
    AARMS, Dalhousie University, Halifax
    August 2015
  • Undergraduate Summer School on Rigorous Computing
    PIMS, Simon-Fraiser University, Vancouver
    June 2015

Teaching activities

Between Fall 2015 and Winter 2018, I was teaching assistant for MATH141 - Calculus 2 (3 times) and MATH133 - Linear Algebra I (1 time), for a total of about 300hrs of teaching, grading, and office hour duties.


Programming Languages

Matlab and C


Spoken Languages

English, French, Chinese, Intermediate German.

Xi-Yuan (Bruce) Yin

I'm a postdoc at the Max Planck Institute for Mathematics in the Sciences (MiS) in Leipzig, where I work in the Applied Analysis group under the mentorship of Prof. László Székelyhidi.

I obtained my PhD in Mathematics at McGill University under the supervision of Prof. Jean-Christophe Nave. I then worked as postdoc at the Fluid Mechanics and Acoustics Laboratory (LMFA) in Lyon under the mentorship of Prof. Wouter Bos.


Research Interests

Most of my work so far is centered around the study of numerical methods for advection dominated problems. While computational fluid mechanics was the principal focus of my reseach, I also have a strong interest for the relevant underlying mathematical theories:

  • Numerical analysis
  • Analysis of partial differential equations
  • Differential geometry (in particular, Geometric Hydrodynamics)


Publications

  • X.-Y. Yin, W. Agoua, T. Wu, W. Bos, The influence of the vorticity-scalar correlation on mixing, (2024) preprint
    [arXiv:2402.16762]
  • S. Taylor, X.-Y. Yin, J.-C. Nave, A functional discretization of the coadjoint action for Euler-Poincaré equations on the diffeomorphism group, (2024)
    in preparation
  • W. Agoua, X.-Y. Yin, T. Wu, W. Bos, Coexistence and persistence of two equilibrium configurations in 2d truncated Euler equations, (2024)
    in preparation
  • P. Krah, X.-Y. Yin, J. Bergmann, J.-C. Nave, K. Schneider, A characteristic mapping method for Vlasov-Poisson with extreme resolution properties, (2024) Comm. Comp. Phys. Volume 35(4) 905-937
    [arXiv:2311.09379]
  • J. Bergmann, T. Maurel-Oujia, X.-Y. Yin, J.-C. Nave, K. Schneider, Singularity formation of vortex sheets in 2d Euler equations using the characteristic mapping method, (2023) preprint
    [arXiv:2404.02008]
  • X.-Y. Yin, K. Schneider, J.-C. Nave, A Characteristic Mapping Method for the three-dimensional incompressible Euler equations, (2023) J. Comp. Phys. Volume 477, 111876
    [arXiv:2107.03504]
  • X.-Y. Yin, O. Mercier, B. Yadav, K. Schneider, J.-C. Nave, A Characteristic Mapping Method for the two-dimensional incompressible Euler equations, (2021) J. Comp. Phys. Volume 424, 109781
    [arXiv:1910.10841]
  • X.-Y. Yin, L. Chen, J.-C. Nave, A Diffusion-Driven Characteristic Mapping Method for Particle Management, (2021) SIAM J. Sci. Comp. Volume 43(5), A3155–A3183
    [arXiv:2008.13076]
  • O. Mercier, X.-Y. Yin, J.-C. Nave, The Characteristic Mapping Method for the linear advection of arbitrary sets, (2020) SIAM J. Sci. Comp. Volume 42(3), A1663-A1685
    [arXiv:1309.2731]
  • I. Balázs, J.B. van den Berg, J. Courtois, J. Dudás, J.P. Lessard, A. Vörös-Kiss, JF Williams, X.-Y. Yin, Computer-assisted proofs for radially symmetric solutions of PDEs, (2020) J. Comp. Dyn. Volume 5, 61-80
    [pdf]

Presentations and Conferences

  • Coexistence of Different Equilibria in 2D Galerkin Truncated Euler Equations
    Réunion du GdR Navier-Stokes 2.00
    Université de Rouen Normandies, October 2023
  • Kelvin-Filtered Turbulence and Relation to Space Locality
    18th European Turbulence Conference
    Universidad Politécnica de Valencia, September 2023
  • Numerical study of high-Reynolds problems using the characteristic mapping method
    Séminaires du LMFA
    École Centrale de Lyon, May 2023
  • Characteristic Mapping method and applications to the singularity problem in the 3D Euler equations
    Réunion du GdR Navier-Stokes 2.00
    École Centrale de Lille, November 2022