Partitioned averaged vector field methods
Partitioned averaged vector field methods
复制标题
分区平均向量场方法
DOI：
10.1016/j.jcp.2018.05.009
复制
发表时间：
2018
影响因子：
4.1
通讯作者：
Wang Yushun
中科院分区：
文献类型：
--
作者：
Cai Wenjun;Li Haochen;Wang Yushun
经典的二阶平均向量场（AVF）方法可以精确地保持哈密顿常微分方程和偏微分方程的能量。然而，AVF方法不可避免地导致全隐式非线性代数方程组的一般非线性系统。为了解决这一缺点，并保持所需的能量保持属性，一阶分区AVF方法，提出了第一次划分的变量分组，然后应用AVF方法一步一步。结合其伴随方法，分别提出了分区AVF合成法和加法，使其精度提高到二阶。两个经典模型方程的具体格式的构造与半隐式，线性隐式的性质，使相当低的成本比原来的AVF方法。此外，对于特定的问题，除了传统的能量守恒之外，还可以产生额外的守恒性质。数值验证进一步证实了我们的结果。
The classic second-order average vector field (AVF) method can exactly preserve the energy for Hamiltonian ordinary differential equations and partial differential equations. 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.