Partitioned averaged vector field methods

JOURNAL OF COMPUTATIONAL PHYSICS

卷:370

Article

Cai, Wenjun¹  Li, Haochen²  Wang, Yushun¹ 

[1] Nanjing Normal Univ, Sch Math Sci, Jiangsu Key Lab NSLSCS, Nanjing 210023, Jiangsu, Peoples R China

[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

关键词: Hamiltonian system;    Energy-preserving scheme;    Averaged vector field method;    Discrete gradient method;   

DOI  :  10.1016/j.jcp.2018.05.009

来源: Elsevier

【 摘 要 】

The classic second-order averaged vector field (AVF) method can exactly preserve the energy for Hamiltonian systems. However, the AVF method inevitably leads to fully-implicit nonlinear algebraic equations for general nonlinear systems. To address this drawback and maintain the desired energy-preserving property, a first-order partitioned AVF method is proposed which first divides the variables into groups and then applies the AVF method step by step. In conjunction with its adjoint method we present the partitioned AVF composition method and plus method respectively to improve its accuracy to second order. Concrete schemes for two classic model equations are constructed with semi-implicit, linear-implicit properties that make considerable lower cost than the original AVF method. Furthermore, additional conservative property can be generated besides the conventional energy preservation for specific problems. Numerical verification of these schemes further conforms our results. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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