Positivity/bound/length preserving schemes for complex nonlinear systems

Speaker：

Jie Shen (Eastern Institute of Technology, Ningbo)

Time：

Tues., 10:00 am, Mar. 25, 2025

Venue：

C548, Shuangqing Complex Building A

Online：

Zoom Meeting ID: 276 366 7254

Passcode: YMSC

Title:

Positivity/bound/length preserving schemes for complex nonlinear systems

Abstract：

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 violation 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 reformulation 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.