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Welcome to Xu Wang's homepage!

Contact Information

Office: MATH736

Telephone: +1 765 49-63178

Email: wang4191@purdue.edu

Mailing address:

Department of Mathematics
Purdue University
150 North University Street
West Lafayette, IN 47907, USA


2013 - 2018: Ph.D. in Computational Mathematics, Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences (CAS)

2009 - 2013: B.S. in Applied Mathematics, Xiamen University

Professional Experience

2021 - now: Assistant Professor, Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC), AMSS, CAS

2018 - 2021: Golomb Visiting Assistant Professor, Purdue University


2020 Fall - 2021 Spring: Math 351, Elementary Linear Algebra, Purdue University [coursepage | syllabus]

2018 Fall - 2020 Spring: Math 265, Linear Algebra, Purdue University [coursepage]

2016: Fundamental Biomedical Signal Processing, Sino-Danish College, University of CAS [coursepage]

Research Interest

Stochastic inverse problems
Direct and inverse scattering problems
Ergodicity and invariant measures for numerical methods of SPDEs
Stochastic symplectic and multi-symplectic methods for SPDEs


- Book -
  1. (with J. Hong) Invariant Measures for Stochastic Nonlinear Schrödinger Equations, Lecture Notes in Mathematics 2251, Springer, Singapore, 2019. [link]


- Journals -
  1. (with P. Li) Regularity of distributional solutions to stochastic acoustic and elastic scattering problems, J. Differential Equations, 285 (2021), 640–662. [pdf]
  2. (with Y. Gong, P. Li, and X. Xu) Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift, Inverse Problems, 37 (2021), 045001. [pdf]
  3. (with P. Li) Inverse random source scattering for the Helmholtz equation with attenuation, SIAM J. Appl. Math., 81 (2021), 485–506. [pdf]
  4. (with P. Li) An inverse random source problem for Maxwell’s equations, Multiscale Model. Simul., 19 (2021), 25–45. [pdf]
  5. (with J. Hong and C. Huang) Optimal rate of convergence for two classes of schemes to stochastic differential equations driven by fractional Brownian motions, IMA J. Numer. Anal., 41 (2021), 1608–1638. [pdf]
  6. (with P. Li) An inverse random source problem for the one-dimensional Helmholtz equation with attenuation, Inverse Problems, 37 (2021), 015009. [pdf]
  7. (with X. Feng and P. Li) An inverse random source problem for the time fractional diffusion equation driven by a fractional Brownian motion, Inverse Problems, 36 (2020), 045008. [pdf]
  8. (with J. Hong, C. Huang, and M. Kamrani) Optimal strong convergence rate of a backward Euler type scheme for the Cox–Ingersoll–Ross model driven by fractional Brownian motion, Stochastic Process. Appl., 130 (2020), 2675–2692. [pdf]
  9. (with C.-E. Bréhier) On parareal algorithms for semilinear parabolic stochastic PDEs, SIAM J. Numer. Anal., 58 (2020), 254–278. [pdf]
  10. (with J. Hong and L. Zhang) Parareal exponential θ-scheme for longtime simulation of stochastic Schödinger equations with weak damping, SIAM J. Sci. Comput., 41 (2019), B1155–B1177. [pdf]
  11. (with J. Hong and C. Huang) Symplectic Runge–Kutta methods for Hamiltonian systems driven by Gaussian rough paths, Appl. Numer. Math., 129 (2018), 120–136. [pdf]
  12. (with J. Hong and L. Sun) High order conformal symplectic and ergodic schemes for the stochastic Langevin equation via generating functions, SIAM J. Numer. Anal., 55 (2017), 3006–3029. [pdf]
  13. (with J. Hong and L. Zhang) Numerical analysis on ergodic limit of approximations for stochastic NLS equation via multi-symplectic scheme, SIAM J. Numer. Anal., 55 (2017), 305–327. [pdf]
  14. (with C. Chen and J. Hong) Approximation of invariant measure for damped stochastic nonlinear Schrödinger equation via an ergodic numerical scheme, Potential Anal., 46 (2017), 323–367. [pdf]
  15. (with J. Cui, Z. Liu, and L. Miao) Hölder continuity for parabolic Anderson equation with non-Gaussian noise, J. Math. Anal. Appl., 441 (2016), 684–691. [pdf]
  16. Read more


- Preprints -
  1. (with J. Li and P. Li) Inverse random potential scattering for elastic waves, arXiv:2102.07062.
  2. (with X. Feng, M. Zhao, and P. Li) An inverse source problem for the stochastic wave equation, arXiv:2101.04744.
  3. (with Y. Chen and P. Li) Analysis of the time-domain PML problem for Maxwell’s equations in a waveguide, arXiv:2009.09337.
  4. (with J. Li and P. Li) Inverse elastic scattering for a random potential, arXiv:2007.05790.
  5. (with J. Hong, L. Ji, and J. Zhang) Stochastic K-symplectic integrators for stochastic non-canonical Hamiltonian systems and applications to the Lotka–Volterra model, arXiv:1711.03258.
  6. (with J. Hong and L. Ji) Convergence in probability of an ergodic and conformal multi-symplectic numerical scheme for a damped stochastic NLS equation, arXiv:1611.08778.
  7. Read more


- Presentations -
  • Web-workshop on numerical PDEs and applications, Taiyuan University of Technology, online, May, 2021.
  • Mini web-workshop on computational inverse problems and applications, Changsha University of Science and Technology, online, April, 2021.
  • Workshop on structure-preserving methods for SPDEs, Academy of Mathematics and Systems Science, CAS, online, April, 2021.
  • Colloquiums and Seminars in Center for Computational and Applied Mathematics, Purdue University, online, February, 2021.
  • Colloquia and Seminars in Academy of Mathematics and Systems Science, CAS, online, December, 2020.
  • Workshop on Theoretical and Computational Analyses for Inverse Problems, Heilongjiang University, online, November, 2020.
  • Web-Workshop on Inverse Problems and Applied Differential Equations, Changsha University of Science and Technology, online, September, 2020.
  • Web-Workshop on Wave Scattering Problems, Beijing University of Technology, online, August, 2020.
  • Mini-Web-Workshop on Stochastic Analysis and Computation, Northeast Normal University, online, May, 2020.
  • Spring Southeastern AMS Sectional Meeting, Auburn University, Auburn, USA, March, 2019.
  • Seminar on Hot Topics in Stochastic Computing, Tianyuan Mathematical Center in Northeast China, Changchun, June, 2018.
  • The 40th Stochastic Processes and Their Applications Conference, Gothenburg, Sweden, June, 2018.
  • The 525th Academic Forum for PhD Students, Tsinghua University, Beijing, April, 2018.
  • Forum on Numerical Analysis for SDEs and SPDEs, AMSS, CAS, Beijing, November, 2017.
  • Efficiency Numerical Methods for Stochastic Hamiltonian Partial Differential Equations, Central South University, Changsha, October, 2017.
  • International Workshop on BSDEs, SPDEs and Their Applications, The University of Edinburgh, Edinburgh, UK, July, 2017.
  • 10th International Conference on Computational Physics, University of Macau, Macau, China, January, 2017.
  • 20th IMACS World Congress, Xiamen University, Xiamen, China, November, 2016.
  • Numerical Analysis of Stochastic Partial Differential Equations, University of Gothenburg, Gothenburg, Sweden, September, 2016.
  • Workshop on Dynamical System and Its Applications, Dalian University of Technology, Dalian, China, March, 2016.
  • Conference on Strucsture-perserving Algorithms, Nanjing Normal University, Nanjing, China, December, 2015.
  • International Workshop on Mathematical Sciences, Dalian University of Technology, Dalian, China, October, 2015.
  • Scientific Computation and Differential Equations, University of Potsdam, Potsdam, Germany, September, 2015.
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