Multi-time-step FDTD method with even factor

2005 ◽  
Author(s):  
Yang-Ming Zheng ◽  
Qing-Xin Chu
Keyword(s):  
Fdtd Method ◽  
Time Step ◽  
Even Factor

scholarly journals Precise-Integration Time-Domain Formulation for Optical Periodic Media

Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7896
Author(s):  
Joan Josep Sirvent-Verdú ◽  
Jorge Francés ◽  
Andrés Márquez ◽  
Cristian Neipp ◽  
Mariela Álvarez ◽  
...  
Keyword(s):  
Time Domain ◽  
Fdtd Method ◽  
Fdtd Simulation ◽  
Integration Time ◽  
Periodic Media ◽  
Step Size ◽  
Time Step ◽  
Precise Integration ◽  
Time Step Size ◽  
Wide Range

A numerical formulation based on the precise-integration time-domain (PITD) method for simulating periodic media is extended for overcoming the Courant-Friedrich-Levy (CFL) limit on the time-step size in a finite-difference time-domain (FDTD) simulation. In this new method, the periodic boundary conditions are implemented, permitting the simulation of a wide range of periodic optical media, i.e., gratings, or thin-film filters. Furthermore, the complete tensorial derivation for the permittivity also allows simulating anisotropic periodic media. Numerical results demonstrate that PITD is reliable and even considering anisotropic media can be competitive compared to traditional FDTD solutions. Furthermore, the maximum allowable time-step size has been demonstrated to be much larger than that of the CFL limit of the FDTD method, being a valuable tool in cases in which the steady-state requires a large number of time-steps.

Optimum time-step size for 2D (2, 4) FDTD method

2011 ◽  
Vol 47 (5) ◽  
pp. 317 ◽  
Author(s):  
T.T. Zygiridis
Keyword(s):  
Fdtd Method ◽  
Step Size ◽  
Time Step ◽  
Optimum Time ◽  
Time Step Size

scholarly journals 3‐D non‐uniform time step locally one‐dimensional FDTD method

2016 ◽  
Vol 52 (12) ◽  
pp. 993-994 ◽  
Author(s):  
Zaifeng Yang ◽  
Eng Leong Tan
Keyword(s):  
Fdtd Method ◽  
Time Step ◽  
One Dimensional

scholarly journals An Efficient Numerical Formulation for Wave Propagation in Magnetized Plasma Using PITD Method

Electronics ◽  
2020 ◽  
Vol 9 (10) ◽  
pp. 1575 ◽  
Author(s):  
Zhen Kang ◽  
Ming Huang ◽  
Weilin Li ◽  
Yufeng Wang ◽  
Fang Yang
Keyword(s):  
Wave Propagation ◽  
Time Domain ◽  
Fdtd Method ◽  
Magnetized Plasma ◽  
Numerical Dispersion ◽  
Step Size ◽  
Time Step ◽  
Precise Integration ◽  
Dispersion Error ◽  
Time Step Size

A modified precise-integration time-domain (PITD) formulation is presented to model the wave propagation in magnetized plasma based on the auxiliary differential equation (ADE). The most prominent advantage of this algorithm is using a time-step size which is larger than the maximum value of the Courant–Friedrich–Levy (CFL) condition to achieve the simulation with a satisfying accuracy. In this formulation, Maxwell’s equations in magnetized plasma are obtained by using the auxiliary variables and equations. Then, the spatial derivative is approximated by the second-order finite-difference method only, and the precise integration (PI) scheme is used to solve the resulting ordinary differential equations (ODEs). The numerical stability and dispersion error of this modified method are discussed in detail in magnetized plasma. The stability analysis validates that the simulated time-step size of this method can be chosen much larger than that of the CFL condition in the finite-difference time-domain (FDTD) simulations. According to the numerical dispersion analysis, the range of the relative error in this method is 10−6 to 5×10−4 when the electromagnetic wave frequency is from 1 GHz to 100 GHz. More particularly, it should be emphasized that the numerical dispersion error is almost invariant under different time-step sizes which is similar to the conventional PITD method in the free space. This means that with the increase of the time-step size, the presented method still has a lower computational error in the simulations. Numerical experiments verify that the presented method is reliable and efficient for the magnetized plasma problems. Compared with the formulations based on the FDTD method, e.g., the ADE-FDTD method and the JE convolution FDTD (JEC-FDTD) method, the modified algorithm in this paper can employ a larger time step and has simpler iterative formulas so as to reduce the execution time. Moreover, it is found that the presented method is more accurate than the methods based on the FDTD scheme, especially in the high frequency range, according to the results of the magnetized plasma slab. In conclusion, the presented method is efficient and accurate for simulating the wave propagation in magnetized plasma.

scholarly journals Full-Wave Analysis of the Shielding Effectiveness of Thin Graphene Sheets with the 3D Unidirectionally Collocated HIE-FDTD Method

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Arne Van Londersele ◽  
Daniël De Zutter ◽  
Dries Vande Ginste
Keyword(s):  
Graphene Sheet ◽  
Open Space ◽  
Fdtd Method ◽  
Critical Dimension ◽  
Shielding Effectiveness ◽  
Time Step ◽  
Full Wave ◽  
Full Wave Analysis ◽  
Electrical Components ◽  
Real Challenge

Graphene-based electrical components are inherently multiscale, which poses a real challenge for finite-difference time-domain (FDTD) solvers due to the stringent time step upper bound. Here, a unidirectionally collocated hybrid implicit-explicit (UCHIE) FDTD method is put forward that exploits the planar structure of graphene to increase the time step by implicitizing the critical dimension. The method replaces the traditional Yee discretization by a partially collocated scheme that allows a more accurate numerical description of the material boundaries. Moreover, the UCHIE-FDTD method preserves second-order accuracy even for nonuniform discretization in the direction of collocation. The auxiliary differential equation (ADE) approach is used to implement the graphene sheet as a dispersive Drude medium. The finite grid is terminated by a uniaxial perfectly matched layer (UPML) to permit open-space simulations. Special care is taken to elaborate on the efficient implementation of the implicit update equations. The UCHIE-FDTD method is validated by computing the shielding effectiveness of a typical graphene sheet.

Numerical Simulation of Nanopulse Penetration of Biological Matters Using the ADI-FDTD Method

2012 ◽  
Author(s):  
Fei Zhu ◽  
Weizhong Dai
Keyword(s):  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Stable Solution ◽  
Biological Tissues ◽  
Computational Time ◽  
Time Step ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Difference Time

Study of the nanopulse bioeffects is important to ensure the appropriate application with nanopulse in biomedical and biotechnological settings. In this article, we develop an alternating-direction implicit (ADI) finite-difference time-domain (FDTD) scheme coupled with the Cole-Cole expression for dielectric coefficients of biological tissues to simulate the electromagnetic fields inside the biological tissues when exposed to nanopulses. The scheme is then tested by numerical examples with two different biological tissues. Numerical results show that the proposed ADI-FDTD scheme breaks through the Courant, Friedrichs, and Lewy (CFL) stability condition and provides a stable solution with a larger time step, where the conventional FDTD scheme fails. Results also indicate that the computational time can be reduced when using a larger time step.

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