The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems

Source abstract

The invariant energy quadratization (IEQ) and scalar auxiliary variable (SAV) approaches are two recently proposed methods to develop linear and unconditionally energy stable schemes for a class of dissipative/conservative systems. The essential idea of these two methods is the energy quadratization strategy, where either the nonlinear potential or its integral is transformed into quadratic forms of the new auxiliary variables. We present the IEQ and SAV approaches in a unified and more general setting, show a few typical applications to problems with moderately stiff nonlinearities, and then present the stabilized IEQ and SAV approaches to deal with several complex systems with highly stiff nonlinear terms.