Volume 3, Issue 6
Multi-Symplectic Wavelet Collocation Method for Maxwell's Equations

Adv. Appl. Math. Mech., 3 (2011), pp. 663-688.

Published online: 2011-03

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• Abstract

In this paper, we develop a multi-symplectic wavelet collocation method for three-dimensional (3-D) Maxwell's equations. For the multi-symplectic formulation of the equations, wavelet collocation method based on autocorrelation functions is applied for spatial discretization and appropriate symplectic scheme is employed for time integration. Theoretical analysis shows that the proposed method is multi-symplectic, unconditionally stable and energy-preserving under periodic boundary conditions. The numerical dispersion relation is investigated. Combined with splitting scheme, an explicit splitting symplectic wavelet collocation method is also constructed. Numerical experiments illustrate that the proposed methods are efficient, have high spatial accuracy and can preserve energy conservation laws exactly.

37M15, 65P10, 65M70, 65T60

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@Article{AAMM-3-663, author = {Zhu , HuajunSong , Songhe and Chen , Yaming}, title = {Multi-Symplectic Wavelet Collocation Method for Maxwell's Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2011}, volume = {3}, number = {6}, pages = {663--688}, abstract = {

In this paper, we develop a multi-symplectic wavelet collocation method for three-dimensional (3-D) Maxwell's equations. For the multi-symplectic formulation of the equations, wavelet collocation method based on autocorrelation functions is applied for spatial discretization and appropriate symplectic scheme is employed for time integration. Theoretical analysis shows that the proposed method is multi-symplectic, unconditionally stable and energy-preserving under periodic boundary conditions. The numerical dispersion relation is investigated. Combined with splitting scheme, an explicit splitting symplectic wavelet collocation method is also constructed. Numerical experiments illustrate that the proposed methods are efficient, have high spatial accuracy and can preserve energy conservation laws exactly.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.11-m1183}, url = {http://global-sci.org/intro/article_detail/aamm/189.html} }
TY - JOUR T1 - Multi-Symplectic Wavelet Collocation Method for Maxwell's Equations AU - Zhu , Huajun AU - Song , Songhe AU - Chen , Yaming JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 663 EP - 688 PY - 2011 DA - 2011/03 SN - 3 DO - http://doi.org/10.4208/aamm.11-m1183 UR - https://global-sci.org/intro/article_detail/aamm/189.html KW - Multi-symplectic, wavelet collocation method, Maxwell's equations, symplectic, conservation laws. AB -

In this paper, we develop a multi-symplectic wavelet collocation method for three-dimensional (3-D) Maxwell's equations. For the multi-symplectic formulation of the equations, wavelet collocation method based on autocorrelation functions is applied for spatial discretization and appropriate symplectic scheme is employed for time integration. Theoretical analysis shows that the proposed method is multi-symplectic, unconditionally stable and energy-preserving under periodic boundary conditions. The numerical dispersion relation is investigated. Combined with splitting scheme, an explicit splitting symplectic wavelet collocation method is also constructed. Numerical experiments illustrate that the proposed methods are efficient, have high spatial accuracy and can preserve energy conservation laws exactly.

Huajun Zhu, Songhe Song & Yaming Chen. (1970). Multi-Symplectic Wavelet Collocation Method for Maxwell's Equations. Advances in Applied Mathematics and Mechanics. 3 (6). 663-688. doi:10.4208/aamm.11-m1183
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