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[Lecture] Highly efficient and accurate structure preserving schemes for complex nonlinear systems

APR . 24 2020
Topic: School Colloquium—Highly efficient and accurate structure preserving schemes for complex nonlinear systems

Time: 
10:00-11:00 AM, April 24, 2020

Speaker: Prof. Jie Shen (Purdue University)

Online address: Tencent Meeting (Room ID: 849-579-539; Link: https://meeting.tencent.com/s/5i7ADbuc0e15)

Abstract: Many complex nonlinear systems have intrinsic structures such as energy dissipation or conservation, and/or positivity/maximum principle preserving. It is desirable, sometimes necessary, to preserve these structures in a numerical scheme.

I will present some recent advances on using the scalar auxiliary variable (SAV) approach to develop highly efficient and accurate structure preserving schemes for a large class of complex nonlinear systems. These schemes can preserve energy dissipation/conservation as well as other global constraints, only require solving decoupled linear equations with constant coefficients at each time step, and can achieve higher-order accuracy.

However, the SAV approach will not preserve positivity or maximum principle. I will then present a strategy to construct efficient energy stable and positivity preserving schemes for certain nonlinear evolution systems, such as the Poisson-Nernst-Planck (PNP) equation and Keller-Segel equation, whose solutions remain to be positive.

Personal homepage: https://www.math.purdue.edu/~shen7/

Source:School of Mathematical Sciences