非局部守恒Allen-Cahn方程的高效算子分裂格式

研究带有拉格朗日乘子的非局部守恒Allen-Cahn方程的高效算子分裂格式.基于算子分裂思想,将原方程分解为非线性方程、非局部方程和拉格朗日乘子方程;然后,利用非线性方程解析求解,非局部方程结合矩形公式及Crank-Nicolson格式建立二阶差分格式,利用拉格朗日乘子方程进行数值积分离散.理论分析表明:数值格式满足质量守恒.最后,通过数值算例验证算法的有效性,包括收敛阶、能量递减及质量守恒.

Effective Operator Splitting Scheme for Conservative Nonlocal Allen-Cahn Equation

An effective operator splitting scheme for solving the nonlocal Allen-Cahn equation with a Lagrange multiplier is studied, based on the operator splitting method, the original equation is discretized respectively into a nonlinear equation, a nonlocal equation and a Lagrange multiplier equation. Then, the nonlinear equation is solved analytically; the nonlocal equation is discreted using rectangle formula and Crank-Nicolson format, and Lagrange multiplier equation is discreted using trapezoidal formulas. The theoretical results show that the proposed scheme satisfies is mass conservation. Numerical experiments demonstrate the validity of the proposed method, including convergence order, energy decline and mass conservation.