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 - <p style="text-align: justify;">In this paper, we develop a multi-symplectic wavelet collocation method for 
three-dimensional (3-D) Maxwell&#39;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.</p>