Professor Jie Shen was invited to give a lecture

发布时间: 2023-12-15 21:12:00

Topic：  BasesPositivity/Bound/Length Preserving Schemes for Complex Nonlinear Svstems

Speaker：Jie Shen

Time：2023-12-12 15:00-16:00

Tencent Meeting ID： 656-4902-4546

Introduction：

    Solutions of a large class of partial differential equations (PDEs) arising from sciences and engineering applications are required to preserve positivity/bound or length, and also energy dissipative. It is of critical importance that their numerical approximations preserve these structures at the discrete level, as yiolation of these structures may render the discrete problems ill posed or inaccurate.

    I will review the existing approaches for constructing positivity/bound preserving schemes, and then present several efficient and accurate approaches: (i) through refor-mulation as Wasserstein gradient flows; (ii) through a suitable functional transform; and (iii) through a Lagrange multiplier, which can also be used to construct length preserving schemes. These approaches have different advantages and limitations, are all relatively easy to implement and can be combined with most spatial discretizations.

Organizer

School of Mathematical Sciences, South China Normal University, Machine Learning and Optimization Computing Laboratory

Co-organizers

Guangdong Young Scientists Association

Guangdong Computational Mathematical Society