期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

Cahn-Hilliard方程的高阶保能量散逸性方法 被引量：2

HIGH ORDER PRESERVING ENERGY-DISSIPATING METHOD OF THE CAHN-HILLIARD EQUATION
原文传递
导出
摘要 能量散逸性是物理和力学中某些微分方程一项重要的物理特性.构造精确地保持微分方程能量散逸性的数值格式对模拟具有能量散逸性的微分方程具有重要的意义.本文利用四阶平均向量场方法和傅里叶谱方法构造了Cahn-Hilliard方程高阶保能量散逸性格式.数值结果表明高阶保能量散逸性格式能很好地模拟Cahn-Hilliard方程在不同初始条件下解的行为,并且很好地保持了Cahn-Hilliard方程的能量散逸特性. Energy-dissipating is a very important physical property of some differential equations in physics and mechanics. It has important meaning in simulating the energy dissipating partial differential equation to constructing a numerical scheme which preserves the energy dissipation property of the differential equation precisely. In this paper,we propose a high order energy-dissipating formula of the Cahn-Hilliard equation by the fourth-order average vector field method and Fourier pseudospeetral method. Numerical results show that the high order preserving energy-dissipating formula can well simulate the behavior of the Cahn- Hilliard equation with different initial conditions and preserve the energy-dissipating property of the Cahn-Hilliard equation.
作者 赵鑫 孙建强 何雪珺
机构地区 海南大学信息科学技术学院
出处 《计算数学》 CSCD 北大核心 2015年第2期137-147,共11页 Mathematica Numerica Sinica
基金 国家自然科学基金(11161017) 海南省自然科学基金(114003)资助
关键词 高阶平均向量场方法 能量散逸性 CAHN-HILLIARD方程 High order average vector field method Energy-dissipating Cahn-Hilliard eauation
分类号 O241.8 [理学—计算数学]
  • 相关文献

参考文献12

  • 1Furihata D. A stable and conservative finite difference scheme for the Cahn-Hilliard equation[J]. Numer. Math., 2001, 87: 675-699.
  • 2Celledoni E, Grimm V, McLachlan R I, McLaren D I, ect Preserving energy resp. dissipation in numerical PDEs, using the average Vector Field method[J]. Comput. Phys., (2012, 231: 6770-6789.
  • 3Bridges T J, Reich S. Numerical methods for Hamiltonian PDEs[J]. J. Phys. A: Math. Gem, 2006, 39: 5287-5320.
  • 4McLachlan R I and Quispel N R W and Robidoux N. Geometric integration using discrete gradi- ents[J]. Phil. Trans. Roy. Soc. A, 1999, 357: 32-56.
  • 5Furihata D, Matsuo T. Discrete variational derivative method, A structure-preserving numerical method for partial differential equations[C]. CRC Press, 2010.
  • 6Quispel G R W and McLaren D I. A new class of energy-preserving numerical integration method[J]. Phys. A: Math. Theor., 2008, 41: 045206(7pp).
  • 7Celledoni E, Mclaren D, McLachlan R I, Owren B, Quispel G R. Wright, Energy-Preserving Methods and B-Series, 21 Nordic Seminar on Computational Mechanics(NSCM-21), 2008.
  • 8Celledoni E, McLachlan R I, Owren B and Quispel G R W. Energy-preserving integrators and the structure of B-series, NTNU Report 5: 2009.
  • 9Chen Jingbo and Qin Mengzhao. multi-symplectic fourier pseudospectral method for the nonlinear schrSdinger equation[J]. Electronic Transactions on Numerical Analysis., 2001, 12: 193-204.
  • 10Briges W L and Henson V E. The DFT:An Owner's Manual for the Discrete Fourier Transform[J]. SIAM, 1995.

二级参考文献9

  • 1郭峰,吴凤珍.MKdV方程的多辛格式[J].河南师范大学学报（自然科学版）,2005,33(1):128-129. 被引量：2
  • 2冯康,秦孟兆.哈密尔顿系统的辛几何算法[M].杭州:浙江科学技术出版社,2002.
  • 3Bridges T.J.Multisymplectic structures and wave propagation[J].Math.Proc.Camb.Phil.Soc.,1999,121:147-190.
  • 4Bridges T.J.,Reich S.Multisymplectic integrators:numerical schemes for Hamiltonian PDEs that conserve symplecticity[J].Phys.Lett.,2001,284:184-193.
  • 5Bridges T.J.,Reich S.Numerical Methods for Hamiltonian PDEs[J].Jo Phys.A:Math.Gen.,2006,39:5287-5320.
  • 6Bridges T.J.,Reich S.Multisymplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations[J].Physica D,2001,152-153:491-504.
  • 7Chen J.B.,Qin M.Z.Multisymplectic Fourier pseudospectral method for the SchrSdinger equa-tion[J].Electronic Transactions on Numerical Analysis,2001,12:193-204.
  • 8Chen J.B.Symplectic and multisymplectic Fourier pseudospectral Discretzation for the Klein-Gordon equation[J].Letters in Mathematical Physics,2006,75:293-305.
  • 9Jian Wang.A note on multisymplectic Fourier pseud0spectral discretization for the nonlinear Schr(o)dinger equation[J].Applied Mathematics and Computation,2007,191:31-41.

共引文献1

同被引文献14

  • 1Furihata D. A stable and conservative finite difference scheme [or the Cahn-Hilliard equation[J]. Numer Math, 2001,87 : 675-699.
  • 2Jaemin S, Seong-Kwan P, Junseok K. A hybrid FEM for solving the Allen-Cahn equation[J]. Applied Mathematics and Computation, 2014,24,1 .. 606-612.
  • 3Bridges T J, Reich S. Numerical methods for Hamiltonian PDEs[J]. Phys A .. Math Gen, 2006,39 .. 5287-5320.
  • 4Cai J X, Wang Y S. Local structure preserving algorithms for the "good" Boussinesq equation[J]. Journal of Comput Phys, 2013,239 : 72-89.
  • 5Celledoni E, Grimm V, Mclachlan R I, et al, Preserving en- ergy resp. dissipation in numerical PDEs using the average vector field method[J]. Journal of Comput Phys, 2012,231 (20) : 6770-6789.
  • 6Quispel G R W, McLaren D I. A new class of energy-pre- serving numerical integration method[J]. Phys A: Math Theor, 2008,41 045206.
  • 7McLachlan R I, Quispel N R W, Robidoux N. Geometric in- tegration using discrete gradents[J]. Phil Trans Roy Soc A, 1999,357 : 32-56.
  • 8Celledoni E, McLachlan R I, Owren B, et al. Energy-preser- ving integrators and the structure of B-series[M] NTNUReport No. 5,2009.
  • 9McLachlan R I, Quispel G R W. Discrete gradient methods have an energy conservation law[J]. Discrete and Continu- ous Dynamical Systems, 2014,, 34 (3) .. 1099-1104.
  • 10Chen J B, Qin M Z. Multi-symplectic Fourier pseudospec- tral method for the nonlinear schr0dinger equation[J]. E- lectronic Transactions on Numerical Anal, 2001,12.. 193- 204.

引证文献2

计算数学
2015年 第2期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部