Energy-conserved splitting FDTD methods for Maxwell’s equations |
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Authors: | Wenbin Chen Xingjie Li Dong Liang |
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Institution: | (1) School of Mathematics, Fudan University, Shanghai, People’s Republic of China;(2) School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA;(3) Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada |
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Abstract: | In this paper, two new energy-conserved splitting methods (EC-S-FDTDI and EC-S-FDTDII) for Maxwell’s equations in two dimensions
are proposed. Both algorithms are energy-conserved, unconditionally stable and can be computed efficiently. The convergence
results are analyzed based on the energy method, which show that the EC-S-FDTDI scheme is of first order in time and of second
order in space, and the EC-S-FDTDII scheme is of second order both in time and space. We also obtain two identities of the
discrete divergence of electric fields for these two schemes. For the EC-S-FDTDII scheme, we prove that the discrete divergence
is of first order to approximate the exact divergence condition. Numerical dispersion analysis shows that these two schemes
are non-dissipative. Numerical experiments confirm well the theoretical analysis results. |
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Keywords: | 65N10 65N15 |
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