This webpage collects information on the STINT Joint China-Sweden Mobility Numerical methods for stochastic partial differential equations CH2016-6729. This mobility program involves the following partners (with main participants in parentheses): Chinese Academy of Sciences (Jialin Hong, Zhou Tao), Central South University (Xiaojie Wang), Chalmers University of Technology and University of Gothenburg (Mihaly Kovacs, Annika Lang, Stig Larsson), and Umeå University (David Cohen).


Informal kick-off meeting at the Chinese Academy of Sciences, Beijing
May 27-28, 2017, Chinese Academy of Sciences, Beijing

In connection with the Forum on Scientific and Engineering Computing 2017.



Visit of a Chinese delegation at Umeå University
October 31 - November 03, 2017, Umeå University, Umeå



Mini-course on Numerical methods for SPDE: strong and weak convergence analysis
November 06-10, 2017, Chinese Academy of Sciences, Beijing

This mini-course is given by Stig Larsson (Göteborg).
The mini-course presents a survey of methods for proving strong convergence and weak convergence of numerical methods for the stochastic heat and wave equations. Strong convergence refers to convergence with respect to a norm, for example, mean square convergence. Proofs typically involve representation of the error using the semigroup theory or energy estimates and using the Ito isometry or the Burkhold--Davies--Gundy inequality. Weak convergence involves the error in some functional of the solution. Proofs may involve representation of the weak error in terms of the Kolmogorov equation and may use integration by parts from the Malliavin calculus. The main part of the lectures will be concerned with the linear stochastic heat and wave equations. As an example of a more difficult problem, we will briefly discuss the stochastic Cahn--Hilliard equation.
Topics covered in this mini-course are:

  • Stochastic integration in Hilbert space. Stochastic evolution problem in Hilbert space. Semigroup, mild solution. Stochastic heat equation. Stochastic wave equation.
  • Numerical approximation by finite elements and Euler's method. Strong convergence.
  • Weak convergence. Malliavin calculus.
  • Stochastic Cahn--Hilliard equation.

    Sponsors

    This mini-course is organised by Jialin Hong and David Cohen within the framework Joint China-Sweden Mobility Grant of the Swedish Foundation for International Cooperation in Research and Higher Education STINT and the National Natural Science Foundation of China NSFC. We gratefully acknowledge its financial support.
    We thank the Institute of Computational Mathematics at the Chinese Academy of Sciences (CAS) for the hospitality.
    Further information can be found here.

    And finally a picture from the classroom:



    Visit of a Swedish delegation at Shandong University (Jinan), Central South University (Changsha) and Hunan Normal (Changsha)
    November 13 - November 17, 2017



    Visit of a Swedish delegation at CAS (Beijing) and Central South University (Changsha)
    May 13 - June 03, 2018



    Scientific event on numerical methods for stochastic partial differential equations
    June 11-15, 2018, Chalmers University of Technology and the University of Gothenburg, Gothenburg

    We organise four sessions on numerical methods for stochastic (partial) differential equations in the 40th Conference on Stochastic Processes and their Applications SPA 2018. Invited speakers: Andrea Barth, Marc Schmidlin, Charles-Edouard Brehier, Lluis Quer-Sardanyons, Raphael Kruse, Andreas Neuenkirch, Michaela Szölgyenyi, Lukasz Szpruch, Adam Andersson, Chuchu Chen, Liying Sun, Jialin Hong, Yanzhao Cao, Felix Lindner, Xu Wang, Jianbo Cui.

    Visit of a Swedish delegation at CAS (Beijing) and forum on numerical analysis of SPDE
    October 10 - October 19, 2018

    Further information on the forum on numerical analysis of SPDE can be found here. Thank you Chuchu for the organisation!
    And the traditional group photo:


    Manuscript submitted
    March 09, 2019

    The work Exponential Integrators for Stochastic Maxwell's Equations Driven by Ito Noise by D. Cohen, J. Cui, J. Hong and L. Sun has been submitted. The manuscript is available here. The original publication is available at www.sciencedirect.com.

    Workshop Numerical Methods for SPDE: 20 successful years and future challenges at the Mittag-Leffler Institute
    May 20-24, 2019

    Details under the following link.

    Manuscript submitted
    July 07, 2019

    The work Drift-preserving numerical integrators for stochastic Hamiltonian systems by C. Chen, D. Cohen, R. D'Ambrosio, and A. Lang has been submitted. The manuscript is available here. The original publication is available at www.link.springer.com.

    Visit of a Swedish delegation at CAS (Beijing), Qufu Normal University (Qufu), Nanchang University (Nanchang), and Central South University (Changsha)
    September 9 - September 25, 2019



    Visit of a Chinese delegation at Chalmers University of Technology (Göteborg)
    November 3 - November 9, 2019



    Online crash course on numerics for SDEs at Central South University (Changsha)
    Fall 2020

    The course is organised by Xiaojie Wang (Central South University, Changsha) and given by David Cohen (Chalmers University of Technology, Göteborg).
    The mini-course is designed to give a concise and accessible introduction to numerical discretisations of stochastic differential equations (SDEs). We assume only a basic competence in calculus and probability theory. Topics: Basics of stochastic processes and SDEs. Numerical methods for SDEs. Strong and weak convergence. Applications.

    The announcement.
    The introductory slides.
    Some figures and photos from the lecture.
    Some computer labs.
    A scan of my lecture notes.

    Time for the online lectures (a zoom link is provided by Xiaojie Wang):
    Tuesday 15 September 2020: 9:00 AM to ca. 11:00 AM, Gothenburg time (15:00-17:00 Beijing time)
    Friday 18 September 2020: 9:00 AM to ca. 11:00 AM, Gothenburg time (15:00-17:00 Beijing time)
    Tuesday 22 September 2020: 9:00 AM to ca. 11:00 AM, Gothenburg time (15:00-17:00 Beijing time)
    Thursday 24 September 2020: 9:00 AM to ca. 11:00 AM, Gothenburg time (15:00-17:00 Beijing time)

    We gratefully acknowledge the additional financial support of the School of Mathematics and Statistics at Central South University.


    Manuscript submitted
    July 06, 2023

    The work Strong convergence rates for a full discretization of stochastic wave equation with nonlinear damping by M. Cai, D. Cohen, and X. Wang has been submitted. The manuscript is available here.


    Workshop Advances in Numerics for S(P)DEs in Gothenburg
    October 14-18, 2024


    The workshop takes place in the room MVL15 at the Department of Mathematical Sciences Chalmers University of Technology

    Preliminary list of participants:
    Chinese Academy of Sciences: Chuchu Chen, Xinyu Chen, Tonghe Dang, Jialin Hong, Ge Liang, Guoting Song, Xu Wang, Guanlin Yang, Fengshan Zhang.
    Capital Normal University: Liying Sun.
    Central South University: Xiaojie Wang.
    Southeast University: Wanrong Cao, Yibo Wang.
    The Hong Kong Polytechnic University: Jianbo Cui.
    NTNU: Øyvind Stormark Auestad.
    Chalmers University of Technology and the University of Gothenburg: David Cohen, Annika Lang, Stig Larsson, Björn Müller, Andrea Papini, Akash Sharma, Johan Ulander.

    The program is here.

    Some photos for concluding this nice week:





    Contacts (Sweden)

    David Cohen

    Department of Mathematical Sciences
    Chalmers University of Technology
    SE-412 96 Göteborg
    and
    Department of Mathematics and Mathematical Statistics
    Umeå universitet
    SE-90187 Umeå

    Annika Lang

    Department of Mathematical Sciences
    Chalmers University of Technology
    SE-412 96 Göteborg


    Last modifications: 18.10.24