A novel relaxed scalar auxiliary variable approach for gradient flows

被引：3

作者：

Liu, Zhengguang ^{[1
]}

He, Qing ^{[1
]}

机构：

[1] Shandong Normal Univ, Sch Math & Stat, Jinan, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2023年 / 141卷

基金：

中国国家自然科学基金;

关键词：

Relaxed scalar auxiliary variable; Energy dissipative law; Gradient flows; Relaxation; Energy stable; Numerical examples; SAV APPROACH; STABILITY; SCHEMES;

D O I：

10.1016/j.aml.2023.108613

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose a novel relaxed scalar auxiliary variable (nRSAV) approach to solve a series of gradient flow problems. The proposed nRSAV approach inherits all the advantages of the traditional SAV and RSAV method. Meanwhile, it preserves a quite close original energy dissipative law and provides an improved accuracy than the baseline SAV method. Besides, compared with the RSAV approach, we do not need to solve a quadratic equation with one unknown to obtain the relaxation. All the semi-discrete schemes are proved to be unconditionally energy stable. Several numerical examples are provided to demonstrate the improved efficiency and accuracy of the proposed method.(c) 2023 Elsevier Ltd. All rights reserved.

引用

页数：8

共 14 条

[1] Scalar Auxiliary Variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrodinger/Gross-Pitaevskii equations [J].

Antoine, Xavier ;

Shen, Jie ;

Tang, Qinglin .

JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 437

[2]

Chen C., 2022, COMPUT MATH APPL

[3]

Chen C., 2022, PLOS ONE, P1

[4] Robust and stable schemes for time fractional molecular beam epitaxial growth model using SAV approach [J].

Hou, Dianming ;

Xu, Chuanju .

JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 445

[5]

Jiang M., 2022, J COMPUT PHYS

[6]

Ju L., 2022, ARXIV

[7] STABILITY AND ERROR ANALYSIS OF IMEX SAV SCHEMES FOR THE MAGNETO-HYDRODYNAMIC EQUATIONS [J].

LI, Xiaoli ;

Wang, Weilong ;

Shen, J. I. E. .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2022, 60 (03) :1026-1054

[8] NEW SAV-PRESSURE CORRECTION METHODS FOR THE NAVIER-STOKES EQUATIONS: STABILITY AND ERROR ANALYSIS [J].

Li, Xiaoli ;

Shen, Jie ;

Liu, Zhengguang .

MATHEMATICS OF COMPUTATION, 2022, 91 (333) :141-167

[9] On efficient semi-implicit auxiliary variable methods for the six-order Swift-Hohenberg model [J].

Liu, Zhengguang ;

Chen, Chuanjun .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2023, 419

[10] THE EXPONENTIAL SCALAR AUXILIARY VARIABLE (E-SAV) APPROACH FOR PHASE FIELD MODELS AND ITS EXPLICIT COMPUTING [J].

Liu, Zhengguang ;

Li, Xiaoli .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2020, 42 (03) :B630-B655

← 1 2 →