scholarly journals On Some Strategies for Computer Simulation of the Wave Propagation Using Finite Differences I. One–Dimensional FDTD Method

2013 ◽  
Vol 64 (4) ◽  
pp. 213-221
Author(s):  
L̓ubomír Šumichrast
Keyword(s):  
Computer Simulation ◽  
Transmission Lines ◽  
Finite Differences ◽  
Fdtd Method ◽  
Numerical Dispersion ◽  
Electromagnetic Plane Wave ◽  
One Dimensional ◽  
Differential Formulation ◽  
The One ◽  
Wave Phenomena

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 discretized form possesses different properties in comparison with the true differential formulation. In this part the issues of stability and numerical dispersion are thoroughly investigated for the one-dimensional case represented here by waves on transmission lines and transversal electromagnetic plane wave

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.

Effect of Metal Intercalating on Transmission Characteristics of One-Dimensional Photonic Crystal

2011 ◽  
Vol 418-420 ◽  
pp. 679-683
Author(s):  
Bei Jia He ◽  
Xin Yi Chen ◽  
Jian Bo Wang ◽  
Jun Lu ◽  
Jian Chang ◽  
...  
Keyword(s):  
Photonic Crystal ◽  
Plasma Frequency ◽  
Fdtd Method ◽  
Transmission Characteristics ◽  
Material Characteristic ◽  
One Dimensional ◽  
Dimensional Photonic Crystal ◽  
Simulation Results ◽  
The One ◽  
Difference Time

To expand the bandgap's width of the one-dimensional photonic crystal, a crystal named SiO2/Metal/MgF2 is formed by joining some metals into the crystal SiO2/MgF2. Furthermore the Finite Difference Time Domain (FDTD) method is used to explore the metals' influence on the crystal's transmission characteristics. The simulation results show that the metals joined could expand the width of the one-dimensional photonic crystal's bandgap effectively and the bandgap's width increases when the metals' thickness increases. Meanwhile the bandgap's characteristic is affected by the metals' material-characteristic. The higher the plasma frequency is, the wider the bandgap's width will be and the more the number of the bandgaps will be. On the other hand, the metals' damping frequency has no significant effect on the bandgap, but would make the bandgap-edge's transmittance decrease slightly.

scholarly journals Optimal Polynomial Decay to Coupled Wave Equations and Its Numerical Properties

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
R. F. C. Lobato ◽  
S. M. S. Cordeiro ◽  
M. L. Santos ◽  
D. S. Almeida Júnior
Keyword(s):  
Decay Rate ◽  
Spectral Methods ◽  
Finite Differences ◽  
Wave Equations ◽  
Coupled System ◽  
Polynomial Decay ◽  
One Dimensional ◽  
Coupled Wave Equations ◽  
Optimal Polynomial ◽  
The One

In this work we consider a coupled system of two weakly dissipative wave equations. We show that the solution of this system decays polynomially and the decay rate is optimal. Computational experiments are conducted in the one-dimensional case in order to show that the energies properties are preserved. In particular, we use finite differences and also spectral methods.

scholarly journals Non-Standard and Numerov Finite Difference Schemes for Finite Difference Time Domain Method to Solve One- Dimensional Schrödinger Equation

2018 ◽  
Vol 2 (1) ◽  
pp. 27
Author(s):  
Lily Maysari Angraini ◽  
I Wayan Sudiarta
Keyword(s):  
Finite Difference ◽  
Harmonic Oscillator ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Finite Difference Schemes ◽  
Potential Wells ◽  
One Dimensional ◽  
The One ◽  
Difference Time

<span>The purpose of  this paper is to show some improvements of the finite-difference time domain (FDTD) method using Numerov and non-standard finite difference (NSFD) schemes for solving the one-dimensional Schr</span><span>ö</span><span>dinger equation. Starting with results of the unmodified FDTD method, Numerov-FD and NSFD are applied iteratively to produce more accurate results for eigen energies and wavefunctios. Three potential wells, infinite square well, harmonic oscillator and Poschl-Teller, are used to compare results of FDTD calculations. Significant improvements in the results for the infinite square potential and the harmonic oscillator potential are found using Numerov-NSFD scheme, and for Poschl-Teller potential are found using Numerov scheme.</span>

Advection-dispersion modelling tools: what about numerical dispersion?

2005 ◽  
Vol 52 (3) ◽  
pp. 19-27 ◽  
Author(s):  
R. Bouteligier ◽  
G. Vaes ◽  
J. Berlamont ◽  
C. Flamink ◽  
J.G. Langeveld ◽  
...  
Keyword(s):  
Dispersion Equation ◽  
Model Calibration ◽  
Suspended Particles ◽  
Numerical Dispersion ◽  
Model Parameters ◽  
One Dimensional ◽  
Advection Dispersion ◽  
The One ◽  
Calibration Tool ◽  
Tracer Experiments

In general the transport of dissolved substances and fine suspended particles is governed by the one-dimensional advection-dispersion equation. In order to model the transport of dissolved substances and fine suspended particles, the advection-dispersion equation is incorporated into commonly used urban drainage modelling tools such as InfoWorks CS (Wallingford Software, United Kingdom) and MOUSE (DHI Software, Denmark). Two examples show the use of InfoWorks CS and MOUSE using standard model settings. Modelling results using tracer experiments show that numerical model parameters need to be altered in order to calibrate the model. Using tracer experiments as a model calibration tool, it is shown that a non-negligible amount of dispersion is generated by InfoWorks CS and MOUSE and that it is in fact the numerical dispersion that is calibrated.

scholarly journals ONE DIMENSIONAL ASYNCHRONOUS COOPERATIVE PARRONDO'S GAMES

2003 ◽  
Vol 03 (04) ◽  
pp. L389-L398 ◽  
Author(s):  
ZORAN MIHAILOVIĆ ◽  
MILAN RAJKOVIĆ
Keyword(s):  
Computer Simulation ◽  
Markov Chain ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Mean Field ◽  
Discrete Time Markov Chain ◽  
One Dimensional ◽  
Field Approach ◽  
The Mean ◽  
The One

A discrete-time Markov chain solution with exact rules for general computation of transition probabilities of the one-dimensional cooperative Parrondo's games is presented. We show that winning and the occurrence of the paradox depends on the number of players. Analytical results are compared to the results of the computer simulation and to the results based on the mean-field approach.

scholarly journals Multiresolution Time-Domain Scheme for Terminal Response of Two-Conductor Transmission Lines

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Zongliang Tong ◽  
Lei Sun ◽  
Ying Li ◽  
Jianshu Luo
Keyword(s):  
Transmission Line ◽  
Transmission Lines ◽  
Time Domain ◽  
Fdtd Method ◽  
Numerical Dispersion ◽  
Dispersion Property ◽  
Scaling Functions ◽  
Terminal Response ◽  
Lossy Transmission ◽  
The Stability

This paper derives a multiresolution time-domain (MRTD) scheme for the two-conductor lossless transmission line equations based on Daubechies’ scaling functions. And a method is proposed to generate the scheme at the terminal and near the terminal of the lines. The stability and numerical dispersion of this scheme are studied, and the proposed scheme shows a better dispersion property than the conventional FDTD method. Then the MRTD scheme is extended to the two-conductor lossy transmission line equations. The MRTD scheme is implemented with different basis functions for both lossless and lossy transmission lines. Numerical results show that the MRTD schemes which use the scaling functions with high vanishing moment obtain more accurate results.

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