SCS: Jeff Banks (RPI)

Thursday Oct 2, 2025, 10:00 AM → 11:00 AM America/New_York

Title: Efficient and accurate structure preserving schemes for complex nonlinear systems 

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, and can achieve higher-order accuracy. The computational cost is dominated by solving decoupled linear equations with constant coefficients at each time step.