An Efficient Operator Splitting Method for Modified Allen-Cahn Equations With Mean Curvature Terms

Cao Zihan; Wu Zhe; Zhai Shuying

doi:10.21656/1000-0887.460107

Volume 47 Issue 7

Jul. 2026

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Cao Zihan, Wu Zhe, Zhai Shuying. An Efficient Operator Splitting Method for Modified Allen-Cahn Equations With Mean Curvature Terms[J]. Applied Mathematics and Mechanics, 2026, 47(7): 924-935. doi: 10.21656/1000-0887.460107

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An Efficient Operator Splitting Method for Modified Allen-Cahn Equations With Mean Curvature Terms

doi: 10.21656/1000-0887.460107

School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P.R. China

Funds:

The National Science Foundation of China(11701196)

Received Date: 2025-05-29
Rev Recd Date: 2025-07-30

Available Online: 2026-07-23

Abstract

Abstract

The modified Allen-Cahn equation with the mean curvature source term can effectively model curvature-driven physical processes. However, the nonlinear term and gradient magnitude make it difficult to design efficient numerical schemes. An efficient numerical scheme was proposed for solving the equation. Based on the Strang operator splitting method, the original equation was discretized in time into three subproblems: the nonlinear equation was solved analytically; the mean curvature equation was discretized using the second-order Runge-Kutta method combined with central differences to establish a fully discrete explicit scheme, while the heat equation was discretized with the Crank-Nicolson method and solved via the alternating direction implicit (ADI) fast scheme. Theoretical analysis shows that, the proposed scheme achieves second order convergence accuracy. Finally, numerical experiments were presented to validate the convergence rate and effectiveness of the scheme.
- modified Allen-Cahn equation,
- operator splitting scheme,
- ADI,
- convergence analysis

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References(33)

References

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