Efficient, linear and fast numerical algorithm for the volume conserved nonlocal Allen-Cahn equation

Abstract

In this article, for the conserved nonlocal Allen-Cahn equation, we construct a set of efficient, linear, unconditionally energy stable numerical schemes based on the Invariant Energy Quadratization approach. We not only show that the proposed schemes satisfy the law of energy dissipation unconditionally, but also derive the error estimates rigorously. Meanwhile, to reduce the computational cost and memory requirement caused by the nonlocal term, a fast implementation process based on the FFT technique is developed. Some numerical simulations are carried out to demonstrate the accuracy and stability of the schemes as well.