An effective operator splitting scheme for two-dimensional conservative nonlocal Allen–Cahn equation

Abstract

An effective operator splitting scheme for solving the nonlocal Allen–Cahn equation with a Lagrange multiplier is studied. Firstly, based on the operator splitting method, the original equation is discretized into a nonlinear equation, a nonlocal equation and a Lagrange multiplier equation, respectively. Then, the nonlinear equation is solved analytically, the nonlocal equation is discretized using Crank–Nicolson format, and the Lagrange multiplier equation is solved explicitly. The mass conservation and convergence analysis of the numerical algorithm are analyzed theoretically. Numerical experiments are presented to confirm the validity of the proposed method, including the convergence, energy decline and mass conservation.