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 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.
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