论文标题
重新审视相位场方程的半图案方案
Revisit of Semi-Implicit Schemes for Phase-Field Equations
论文作者
论文摘要
在各种计算中使用半图案方案是一种非常普遍的做法，这些计算中隐式和非线性术语明确处理所选的线性术语。对于相位方程，对主要椭圆操作员进行隐式处理以减少相关的稳定性约束，而非线性项仍被明确处理，以避免在每个时间步骤求解非线性方程的昂贵过程。但是，最近的数值分析很少与半图计划有关，而“稳定”方案变得非常流行。在这项工作中，我们将考虑具有{\ em一般电位}函数的Allen-Cahn方程的半图案方案。将证明，最大原理是有效的，并且能量稳定性也适用于数值解决方案。本文扩展了Tang \＆Yang的结果（J.Comput。Math。，34（5）：471--481，2016），研究了用{\ em em polynomial势}的Allen-Cahn方程的半密码方案}。
It is a very common practice to use semi-implicit schemes in various computations, which treat selected linear terms implicitly and the nonlinear terms explicitly. For phase-field equations, the principal elliptic operator is treated implicitly to reduce the associated stability constraints while the nonlinear terms are still treated explicitly to avoid the expensive process of solving nonlinear equations at each time step. However, very few recent numerical analysis is relevant to semi-implicit schemes, while "stabilized" schemes have become very popular. In this work, we will consider semi-implicit schemes for the Allen-Cahn equation with {\em general potential} function. It will be demonstrated that the maximum principle is valid and the energy stability also holds for the numerical solutions. This paper extends the result of Tang \& Yang (J. Comput. Math., 34(5):471--481, 2016) which studies the semi-implicit scheme for the Allen-Cahn equation with {\em polynomial potentials}.
