Decoupled, linear and positivity-preserving schemes for a modified phase field crystal system incorporating long-range interactions

In this article, we aim to establish the linear, decoupled, unconditionally energy stable and positivity-preserving approaches for a modified phase field crystal system incorporating longrange interactions, encompassing diffusive dynamics and elastic interactions. These schemes utilize a generalized positive auxiliary variable technique to explicitly handle nonlinear term, resulting in decoupled linear problems with consistent coefficients at every time step. The unconditional stability property is about the modified discrete energy, rather than the original free energy of the system. Numerical simulations are conducted to confirm the precision and effectiveness of our proposed schemes.