New energy identities and super convergence analysis of the energy conserved splitting FDTD methods for 3D Maxwell's equations

2012 ◽  
Vol 36 (4) ◽  
pp. 440-455 ◽  
Author(s):  
Liping Gao ◽  
Xingjie Li ◽  
Wenbin Chen
Keyword(s):  
Convergence Analysis ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
New Energy ◽  
Fdtd Methods ◽  
Super Convergence

New Energy-Conserved Identitiesand Super-Convergence of the Symmetric Ec-S-Fdtd Scheme for Maxwell’s Equations in 2D

2012 ◽  
Vol 11 (5) ◽  
pp. 1673-1696 ◽  
Author(s):  
Liping Gao ◽  
Dong Liang
Keyword(s):  
Electric Fields ◽  
Maxwell’S Equations ◽  
Numerical Experiments ◽  
Maxwell's Equations ◽  
New Energy ◽  
Efficient Scheme ◽  
Second Order Convergence ◽  
The Magnetic Field ◽  
Super Convergence ◽  
Theoretical Results

AbstractThe symmetric energy-conserved splitting FDTD scheme developed in is a very new and efficient scheme for computing the Maxwell’s equations. It is based on splitting the whole Maxwell’s equations and matching the x-direction and y-direction electric fields associated to the magnetic field symmetrically. In this paper, we make further study on the scheme for the 2D Maxwell’s equations with the PEC boundary condition. Two new energy-conserved identities of the symmetric EC-S-FDTD scheme in the discrete H1-norm are derived. It is then proved that the scheme is uncondi-tionally stable in the discrete H1-norm. By the new energy-conserved identities, the super-convergence of the symmetric EC-S-FDTD scheme is further proved that it is of second order convergence in both time and space steps in the discrete H1-norm. Numerical experiments are carried out and confirm our theoretical results.

Energy-conserved splitting FDTD methods for Maxwell’s equations

2007 ◽  
Vol 108 (3) ◽  
pp. 445-485 ◽  
Author(s):  
Wenbin Chen ◽  
Xingjie Li ◽  
Dong Liang
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Fdtd Methods

scholarly journals Modified Splitting FDTD Methods for Two-Dimensional Maxwell’s Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Liping Gao ◽  
Shouhui Zhai
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
Scattering Problem ◽  
Fdtd Method ◽  
Second Order ◽  
Numerical Dispersion ◽  
Two Dimensional ◽  
Fourier Methods ◽  
Fdtd Methods

In this paper, we develop a new method to reduce the error in the splitting finite-difference method of Maxwell’s equations. By this method two modified splitting FDTD methods (MS-FDTDI, MS-FDTDII) for the two-dimensional Maxwell equations are proposed. It is shown that the two methods are second-order accurate in time and space and unconditionally stable by Fourier methods. By energy method, it is proved that MS-FDTDI is second-order convergent. By deriving the numerical dispersion (ND) relations, we prove rigorously that MS-FDTDI has less ND errors than the ADI-FDTD method and the ND errors of ADI-FDTD are less than those of MS-FDTDII. Numerical experiments for computing ND errors and simulating a wave guide problem and a scattering problem are carried out and the efficiency of the MS-FDTDI and MS-FDTDII methods is confirmed.

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