Numerical Dispersion in the "Complex-Envelope" FDTD Methods and the Sampling Theorem

2006 ◽  
Author(s):  
L'ubomir Sumichrast
Keyword(s):  
Sampling Theorem ◽  
Numerical Dispersion ◽  
Complex Envelope ◽  
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.

scholarly journals On Some Aspects of the Complex–Envelope Finite–Differences Simulation of Wave Propagation in One–Dimensional Case

2014 ◽  
Vol 65 (5) ◽  
pp. 265-270
Author(s):  
L’ubomír Šumichrast
Keyword(s):  
Time Domain ◽  
Electromagnetic Waves ◽  
Numerical Dispersion ◽  
Dimensional Case ◽  
Implicit Methods ◽  
One Dimensional ◽  
Complex Envelope ◽  
Waves Propagation ◽  
The Stability ◽  
The One

Abstract Some aspects of the numerical modeling of the electromagnetic waves propagation using the “complex-envelope” finitedifferences formulation in the one-dimensional case are here reviewed and discussed in comparison with the standard finitedifferences in time-domain (FDTD) approach. The main focus is put on the stability and the numerical dispersion issues of the “complex envelope” explicit and implicit methods

scholarly journals New approach to far field analysis for radiation pattern estimation using FDTD method

2014 ◽  
Vol 11 (4) ◽  
pp. 661-672 ◽  
Author(s):  
Bojana Nikolic ◽  
Bojan Dimitrijevic ◽  
Slavoljub Aleksic ◽  
Nebojsa Raicevic ◽  
Nenad Milosevic
Keyword(s):  
Radiation Pattern ◽  
Fdtd Method ◽  
Field Analysis ◽  
High Order Accuracy ◽  
Numerical Dispersion ◽  
Fdtd Simulation ◽  
Efficient Computation ◽  
New Approach ◽  
Complex Envelope ◽  
General Complex

In this paper an approach to efficient computation of radiation pattern in FDTD simulation environment is presented. A necessary large distance from the radiating object is achieved by multigrid space discretization with unilaterally connected subdomains. A numerical dispersion is reduced using more general complex-envelope finite difference time domain (CE-FDTD) formulation and high order accuracy FDTD schemes where possible. In order to examine how much the introduced algorithm complexity and increased demands concerning computational power and memory are justified by the gain in accuracy, several different scenarios were considered.

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