保守性Allen-Cahn方程的四阶保结构方法

IF 1.5 4区工程技术 Q2 MATHEMATICS, APPLIED

Advances in Applied Mathematics and Mechanics Pub Date : 2023-01-01 DOI:10.4208/aamm.oa-2021-0325

Xiaowei Chen, Xu Qian null, Songhe Song

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引用次数: 1

摘要

．我们提出了一类具有非局部拉格朗日乘子的保守Allen-Cahn方程的最高四阶最大保原理和最大保质量方案。基于空间方向上的二阶有限差分半离散化，在时间方向上采用积分因子龙格-库塔格式。理论分析表明，所提方案在合理的时间步长限制下，与空间步长无关，能保持质量守恒和最大原则。最后，通过数值算例验证了理论分析的正确性。

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Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation

. We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier. Based on the second-order ﬁnite-difference semi-discretization in the spatial direction, the integrating factor Runge-Kutta schemes are applied in the temporal direction. Theoretical analysis indicates that the proposed schemes conserve mass and preserve the maximum principle under reasonable time step-size restriction, which is independent of the space step size. Finally, the theoretical analysis is veriﬁed by several numerical examples.

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来源期刊

Advances in Applied Mathematics and Mechanics MATHEMATICS, APPLIED-MECHANICS

CiteScore

2.60

自引率

7.10%

发文量

审稿时长

6 months

期刊介绍： Advances in Applied Mathematics and Mechanics (AAMM) provides a fast communication platform among researchers using mathematics as a tool for solving problems in mechanics and engineering, with particular emphasis in the integration of theory and applications. To cover as wide audiences as possible, abstract or axiomatic mathematics is not encouraged. Innovative numerical analysis, numerical methods, and interdisciplinary applications are particularly welcome.