Multi-symplectic methods for membrane free vibration equation

Wei Peng Hu; Zi Chen Deng; Wen Cheng Li

doi:10.1007/s10483-007-0906-z

Multi-symplectic methods for membrane free vibration equation

Wei Peng Hu, Zi Chen Deng, Wen Cheng Li

School of Aeronautics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

In this paper, the multi-symplectic formulations of the membrane free vibration equation with periodic boundary conditions in Hamilton space are considered. The complex method is introduced and a semi-implicit twenty-seven-points scheme with certain discrete conservation laws-a multi-symplectic conservation law (CLS), a local energy conservation law (ECL) as well as a local momentum conservation law (MCL)-is constructed to discrete the PDEs that are derived from the membrane free vibration equation. The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior.

Original language	English
Pages (from-to)	1181-1189
Number of pages	9
Journal	Applied Mathematics and Mechanics (English Edition)
Volume	28
Issue number	9
DOIs	https://doi.org/10.1007/s10483-007-0906-z
State	Published - Sep 2007

Keywords

Complex discretization
Multi-symplectic
Runge-Kutta methods

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10.1007/s10483-007-0906-z

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abstract = "In this paper, the multi-symplectic formulations of the membrane free vibration equation with periodic boundary conditions in Hamilton space are considered. The complex method is introduced and a semi-implicit twenty-seven-points scheme with certain discrete conservation laws-a multi-symplectic conservation law (CLS), a local energy conservation law (ECL) as well as a local momentum conservation law (MCL)-is constructed to discrete the PDEs that are derived from the membrane free vibration equation. The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior.",

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AU - Deng, Zi Chen

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AB - In this paper, the multi-symplectic formulations of the membrane free vibration equation with periodic boundary conditions in Hamilton space are considered. The complex method is introduced and a semi-implicit twenty-seven-points scheme with certain discrete conservation laws-a multi-symplectic conservation law (CLS), a local energy conservation law (ECL) as well as a local momentum conservation law (MCL)-is constructed to discrete the PDEs that are derived from the membrane free vibration equation. The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior.

KW - Complex discretization

KW - Multi-symplectic

KW - Runge-Kutta methods

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JO - Applied Mathematics and Mechanics (English Edition)

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ER -

Multi-symplectic methods for membrane free vibration equation

Abstract

Keywords

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