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PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2008-06-06
Maxwell's Equations, Symplectic Matrix, and Grid
By
Wei Sha,

    Dr. Wei Sha

    Anhui University

    China

    Homepage

Xian-Liang Wu,

    Dr. Xian-Liang Wu

    Anhui University

    China

    Homepage

Zhixiang Huang,

    Dr. Zhixiang Huang

    Anhui University

    China

    Homepage

Ming-Sheng Chen

    Dr. Ming-Sheng Chen

    Hefei Teachers College

    China

    Homepage

Progress In Electromagnetics Research B, Vol. 8, 115-127, 2008
doi:10.2528/PIERB08052303 | Google Scholar

Abstract
The connections between Maxwell's equations and symplectic matrix are studied. First, we analyze the continuous-time Maxwell's differential equations in free space and verify its time evolution matrix (TEMA) is symplectic-unitary matrix for complex space or symplectic-orthogonal matrix for real space. Second, the spatial differential operators are discretized by pseudo-spectral (PS) approach with collocated grid and by finite-difference (FD) method with staggered grid. For the PS approach, the TEMA conserves the symplectic-unitary property. For the FD method, the TEMA conserves the symplectic-orthogonal property. Finally, symplectic integration scheme is used in the time direction. In particular, we find the symplectiness of the TEMA also can be conserved. The mathematical proofs presented are helpful for further numerical study of symplectic schemes.
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Citation
Wei Sha, Xian-Liang Wu, Zhixiang Huang, and Ming-Sheng Chen, "Maxwell's Equations, Symplectic Matrix, and Grid," Progress In Electromagnetics Research B, Vol. 8, 115-127, 2008.
doi:10.2528/PIERB08052303
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