应用数学2025，Vol.38Issue(3)：651-669,19.
基于有限差分法利用离散余弦/正弦变换求解泊松方程的快速算法
A Fast Algorithm for Solving the Poisson Equations Based on the Discrete Cosine/Sine Transforms in the Finite Difference Method
摘要
Abstract
To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90％.关键词
相场模型/有限差分法/快速泊松求解器(离散余弦变换/离散正弦变换)/显式不变能量二次化方法/无条件能量稳定性Key words
Phase-field model/Finite difference method/Fast Poisson solver(DC-T/DST)/Explicit invariant energy quadratization/Unconditional energy stability分类
数学引用本文复制引用
李聪聪,王旦霞,贾宏恩,张晨辉..基于有限差分法利用离散余弦/正弦变换求解泊松方程的快速算法[J].应用数学,2025,38(3):651-669,19.基金项目
Supported by Shanxi Province Natural Science Research(202203021212249),Spe-cial/Youth Foundation of Taiyuan University of Technology(2022QN101),National Natural Science Foun-dation of China(12301556),Research Project Supported by Shanxi Scholarship Council of China(2021-029),International Cooperation Base and Platform Project of Shanxi Province(202104041101019),Basic Research Plan of Shanxi Province(202203021211129) （202203021212249）
