守恒型非局部Swift-Hohenberg方程的高效算子分裂格式  

An efficient operator splitting scheme for the conservative nonlocal Swift-Hohenberg equation

作　　者：崔晨 汪亚楠 翟术英 CUI Chen;WANG Yanan;ZHAI Shuying(School of Mathematical Sciences,Huaqiao University,Quan zhou 362021,China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《纯粹数学与应用数学》2024年第3期537-547,共11页Pure and Applied Mathematics

基　　金：国家自然科学基金(11701196);福建省自然科学面上基金(2020J01074).

摘　　要：本文研究带有拉格朗日乘子的守恒型非局部Swift-Hohenberg方程.由于拉格朗日乘子和非局部项的影响,传统的数值求解格式并不能有效求解此方程.本文基于算子分裂方法,设计求解守恒型非局部Swift-Hohenberg方程的高效数值格式:将此方程分解为三个子问题,根据每个子问题的性质选择合理有效的数值求解格式.此方法便于实施且非迭代,在每个时间步长仅需要求解三个解耦的子方程.理论分析表明数值格式满足质量守恒且子问题具有稳定性.最后,通过数值实验验证算法的有效性.The conservative nonlocal Swift-Hohenberg equation with a Lagrange multiplier is studied in this paper.Due to the influence of Lagrange multiplier and nonlocal term,the traditional numerical schemes can not effectively solve this equation.Based on the operator splitting method,an effective numerical scheme for solving the conservative nonlocal Swift-Hohenberg equation is designed.The original equation is discretized into three subproblems,reasonable and effective numerical methods are selected according to the properties of each subproblem.The method is easy to implement and non-iterative,where one only needs to solve three decoupled equations at each time step.The mass conservation of the numerical algorithm and stability of the subproblems are analyzed theoretically.Numerical experiments are presented to confirm the accuracy and efficiency of the proposed method.

关 键 词：非局部Swift-Hohenberg方程 拉格朗日乘子 算子分裂方法 质量守恒 

分 类 号：O241.82[理学—计算数学]