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 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

Fully Coupled Time Domain Modelling of 3D Floating Bodies and Mooring Systems in Regular and Irregular Sea States

2012 ◽  
Author(s):  
Kameswara S. Vepa ◽  
Diederik Van Nuffel ◽  
Wim Van Paepegem ◽  
Joris Degrieck
Keyword(s):  
Time Domain ◽  
Domain Size ◽  
Floating Body ◽  
Computational Time ◽  
Floating Bodies ◽  
Step Size ◽  
Coupled Models ◽  
Time Step ◽  
Time Step Size ◽  
Fully Coupled

Research on floating bodies like Wave Energy Converters (WECs) and Laser Imaging Detection And Ranging (LIDAR) systems has recently known a large growth. To study the minute details of the working model, it is important to study the effect of interactions between the waves, floating bodies and the mooring systems that are controlling the motion of the floating body. To achieve a more realistic numerical model in the time domain, a number of programs are linked together. The idea is to use the strength of each individual program for better results and also reduce the computational time. This paper provides a solution in the direction of using a fully coupled time domain coupling code that controls the data flow between a fluid solver, a structural solver, and a kinematic system simulator. Two- and three-dimensional fully coupled models are studied for calculation times and accuracy of results, and scaling is tested through parallelization on a large HPC cluster. The time step size of the whole model can be controlled by the user. Calculation times and memory requirements vary largely based on the factors like: domain size, SPH particle size, material model used for the floating body and the mooring system, complexity of the mechanical system inside the floating body. As a test case, a rigid body model is presented in this paper.

The impact of the inverse chirp z-transform on breast microwave radar image reconstruction

2020 ◽  
Vol 12 (9) ◽  
pp. 848-854
Author(s):  
Tyson Reimer ◽  
Mario Solis-Nepote ◽  
Stephen Pistorius
Keyword(s):  
Image Reconstruction ◽  
Time Domain ◽  
Tumor Response ◽  
Imaging System ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Inverse Discrete Fourier Transform ◽  
Microwave Radar ◽  
The Impact

This work examines the impact of the inverse chirp z-transform (ICZT) for frequency-to-time-domain conversion during image reconstruction of a pre-clinical radar-based breast microwave imaging system operating over 1–8 GHz. Two anthropomorphic breast phantoms were scanned with this system, and the delay-multiply-and-sum beamformer was used to reconstruct images of the phantoms, after using either the ICZT or the inverse discrete Fourier transform (IDFT) for frequency-to-time domain conversion. The contrast, localization error, and presence of artifacts in the reconstructions were compared. The use of the IDFT resulted in prominent ring artifacts that were not present when using the ICZT, and the use of the ICZT resulted in higher contrast between the tumor and clutter responses. In one of the phantoms, the tumor response was only visible in reconstructions that used the ICZT. The use of the ICZT evaluated with a time-step size of 11 ps resulted in the reduction of prominent artifacts present when using the IDFT and the successful identification of the tumor response in the reconstructed images.

scholarly journals On Some Strategies for Computer Simulation of Thewave Propagation Using Finite Differences II. Multi–Dimensional FDTD Method

2013 ◽  
Vol 64 (6) ◽  
pp. 337-345
Author(s):  
Ľubomír Šumichrast
Keyword(s):  
Computer Simulation ◽  
Wave Propagation ◽  
Wave Equation ◽  
Time Domain ◽  
Finite Differences ◽  
Fdtd Method ◽  
Three Dimensional ◽  
Numerical Dispersion ◽  
Differential Formulation ◽  
Wave Phenomena

Abstract Some strategies used in the computer simulation of wave phenomena by means of finite differences in time-domain (FDTD) method are reviewed and discussed here. It is shown that the wave equation in its discretised form possesses different properties in comparison with the true differential formulation. In this part the issues of stability and numerical dispersion for two- and three-dimensional case of wave propagation in homogeneous space are thoroughly investigated.

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

An efficient application of PML in fourth-order precise integration time domain method for the numerical solution of Maxwell's equations

2013 ◽  
Vol 33 (1/2) ◽  
pp. 116-125
Author(s):  
Zhongming Bai ◽  
Xikui Ma ◽  
Xu Zhuansun ◽  
Qi Liu
Keyword(s):  
Finite Difference ◽  
Numerical Solution ◽  
Fourth Order ◽  
Time Domain ◽  
Fdtd Method ◽  
Time Domain Method ◽  
Integration Time ◽  
Precise Integration ◽  
Content Type ◽  
Domain Method

Purpose – The purpose of the paper is to introduce a perfectly matched layer (PML) absorber, based on Berenger's split field PML, to the recently proposed low-dispersion precise integration time domain method using a fourth-order accurate finite difference scheme (PITD(4)). Design/methodology/approach – The validity and effectiveness of the PITD(4) method with the inclusion of the PML is investigated through a two-dimensional (2-D) point source radiating example. Findings – Numerical results indicate that the larger time steps remain unchanged in the procedure of the PITD(4) method with the PML, and meanwhile, the PITD(4) method employing the PML is of the same absorbability as that of the finite-difference time-domain (FDTD) method with the PML. In addition, it is also demonstrated that the later time reflection error of the PITD(4) method employing the PML is much lower than that of the FDTD method with the PML. Originality/value – An efficient application of PML in fourth-order precise integration time domain method for the numerical solution of Maxwell's equations.

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