TY - JOUR
T1 - A Conformal Energy-Conserved Method for Maxwell's Equations with Perfectly Matched Layers
JO - Communications in Computational Physics
VL - 1
SP - 84
EP - 106
PY - 2018
DA - 2018/09
SN - 25
DO - http://doi.org/10.4208/cicp.OA-2017-0219
UR - https://global-sci.org/intro/article_detail/cicp/12664.html
KW - Maxwell's equations, Fourier pseudo-spectral method, error estimate, conformal conservation
law, PML.
AB - <p style="text-align: justify;">In this paper, a conformal energy-conserved scheme is proposed for solving
the Maxwell&#39;s equations with the perfectly matched layer. The equations are split as a
Hamiltonian system and a dissipative system, respectively. The Hamiltonian system
is solved by an energy-conserved method and the dissipative system is integrated exactly.
With the aid of the Strang splitting, a fully-discretized scheme is obtained. The
resulting scheme can preserve the five discrete conformal energy conservation laws
and the discrete conformal symplectic conservation law. Based on the energy method,
an optimal error estimate of the scheme is established in discrete L<sup>2</sup>-norm. Some numerical
experiments are addressed to verify our theoretical analysis.</p>