Mathematics

CLC number: O241.82

Energy Stable BDF2-SAV Scheme on Variable Grids for the Epitaxial Thin Film Growth Models

外延薄膜生长模型的变时间步长能量稳定的BDF2-SAV格式

Department of Basic Course, Nanjing Audit University Jinshen College, Nanjing 210023, Jiangsu, China

Received: 18 February 2024

Abstract

The second-order backward differential formula (BDF2) and the scalar auxiliary variable (SAV) approach are applied to construct the linearly energy stable numerical scheme with the variable time steps for the epitaxial thin film growth models. Under the step-ratio condition 0$<{\tau }_n/{\tau }_{n-\mathrm{1}}<$4.864, the modified energy dissipation law is proven at the discrete levels with regardless of time step size. Numerical experiments are presented to demonstrate the accuracy and efficiency of the proposed numerical scheme.

摘要

结合二阶向后欧拉公式(BDF2)和标量辅助变量法(SAV)，对外延薄膜生长模型建立变步长线性化能量稳定数值格式。当步长比满足0$<{\tau }_n/{\tau }_{n-\mathrm{1}}<$4.864时，证明了数值格式的修正能量无条件逐层耗散。通过数值算例验证了数值格式的精确性和有效性。