Mathematics Colloquium -- Efficient and Accurate Structure Preserving Schemes for Nonlinear Systems
This event is in the past.
Detroit, MI 48202
Title: Efficient and accurate structure preserving schemes for complex nonlinear systems
Speaker: Jie Shen, Purdue University
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 and Lagrange multiplier 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 and/or are positivity/bound preserving, only require solving decoupled linear equations with constant coefficients at each time step, and can achieve higher-order accuracy.