Squared-SAV schemes for Allen-Cahn equation

Inspired by the recently proposed exponential Scalar Auxiliary Variable (ESAV) schemes, in this work we develop a novel SAV scheme for Allen-Cahn equation that always produces positive values for the scalar auxiliary variable. However, unlike the ESAV schemes, our scheme does not make use of exponential functions at all, which is observed to produce large errors. We prove the unconditional stability of the time-discrete scheme and present two representative numerical examples.