Arnaud Thiry

Numerical Noise Introduced by the Alternating Direction - Implicit Scheme in FDTD for UWB systems

The numerical noise for spherical wave Ultra WideBand (UWB) signals originating from the Alternating Direction-Implicit (ADI) Finite Difference Time Domain (FDTD) scheme is quantified. A practical assessment is then provided to evaluate the numerical noise of the ADI-FDTD method relative to the FDTD method. The study reveals the influence of the temporal and spatial discretisation in conjunction with the maximum frequency of the excitation on the numerical noise. The result can be used for the determination of the temporal discretisation for the acceptable numerical noise increase compared with FDTD prior to running any simulation.

Local velocity calculation for spherical wave UWB signals in FDTD

This paper proposes a procedure to calculate the local propagation speed of a spherical wave UWB signal for the assessment of numerical noise in a limited FDTD space. This method overcomes the theoretical deficiency of phase and group velocities which assumes the plane wave monochromatic signal propagation. The proposed method can estimate the local signal velocity to any propagation directions in one numerical simulation

EFFICIENT ABC FOR THE FREQUENCY DEPENDENT ALTERNATING DIRECTION-IMPLICIT FDTD METHOD

Ultra WideBand (UWB) signals have a high potential for a wide range of applications. The Finite-Difference Time-Domain (FDTD) method is widely used in the development of UWB technology but has still two main limitations. One is that material parameters are constant over the whole frequency range. Frequency dependent materials can be accommodated by adopting a Debye model. The other is that the minimum simulation time is bound by the Courant-Friedrichs-Lewy (CFL) condition, which can be solved by the application of the Alternating Direction-Implicit (ADI) scheme. The combination of Debye model and ADI scheme in FDTD results in the Frequency-Dependent (FD) ADI-FDTD method. This paper proposes an adaptation of the most effective Absorbing Boundary Condition (ABC), the Complex Frequency-Shift (CFS) Perfectly Matched Layer (PML), to FD-ADI-FDTD. The formulation of CFS-PML for FD-ADI-FDTD is proposed and its performance is assessed. The influence of the Courant Number (CFLN), the media parameters and the number of layers are investigated.

Efficient absorbing boundary condition for UWB simulation in frequency dependent ADI-FDTD

UWB simulations require a very efficient ABC which can cope with evanescent waves. CFS-PML is the most complete ABC and can accommodate the high bandwidth of UWB and the evanescent waves coming from a lossy media. Although a CFS-PML formulation has been presented for FDTD and ADI-FDTD, no formulation exists for ADI-FDTD with Debye media. This paper proposed such formulation of CFS-PML to accommodate Debye media in the ADI-FDTD scheme. Further research is currently undergone to assess this ABC and results will be shown at the symposium

Guideline for a UWB waveform robust to the numerical dispersion in FDTD schemes

Research and development of ultra wideband (UWB) systems require model simulations to verify algorithms applied to the systems. In this field, the finite difference time domain (FDTD) method is widely used for simulation of transient wave propagation. The waveforms obtained from FDTD do not perfectly match theoretical ones. Using the assessment of 5 distinctive waveforms, the paper demonstrates that the UWB waveform has a significant bearing on the numerical dispersion. This observation gives a guide for the production of UWB waveforms relatively robust to numerical dispersion in FDTD. The numerical dispersion level proves to be function of the spatial resolution, /spl chi/, and the energy distribution of the source in the frequency domain. Although the waveforms with low -3 dB bandwidth tend to have low numerical dispersion, the maximum frequency in the spectrum also holds a significant influence on the numerical dispersion. This suggests the possibility of estimating the level of the numerical dispersion from the whole spectrum with a given /spl chi/.

Determination and application of signal velocity for spherical wave UWB signals in FDTD

This paper proposes a numerical technique to calculate the local propagation velocity of a spherical wave UWB signal in a limited FDTD space. This method can calculate the velocity at any point to any propagation directions. Meaningful results can be obtained from the method using even a limited number of grid cells which can be accommodated by a single standard desktop machine. This velocity is a function of propagation distance and the pulse shape. As long as the significant evolution of pulse shape is present due to the numerical noise, the local signal velocity varies continually as the pulse propagates. Pulse shape, in other words the frequency range a pulse occupies, affects the propagation distance at which the pulse dispersion becomes mature. This paper makes a link between the pulse shape and observation area where the waveform evolution saturates. The obtained propagation speed can be used for the asymmetry assessment as is done with the phase velocity. An example of propagation speed used for another purpose is also presented

Optimization of CFS-PML Parameters for FD-ADI-FDTD

The frequency dependent alternating direction-implicit finite difference time domain (FD-ADI-FDTD) method is designed to handle FD materials and there is to date no study of the influence of FD materials on the complex frequency-shifted perfectly matched layer (CFS-PML) parameters. This paper studies the effects of the CFS-PML parameters on the reflection coefficient with regard to the FD media parameters

Determination of the CFL number for FD-ADI-FDTD based on the required accuracy

Ultra wideband (UWB) systems have a wide range of applications from microwave imaging to communication purposes. Major advances towards the realization of these applications require a system modeling which produces UWB signal waveforms after propagation in a lossy media. The frequency dependent (FD) finite difference lime domain (FDTD) method is a popular method to do so but is faced with the Courant-Friedrichs-Levy (CFL) condition which limits its time discretisation size. The alternating direction implicit (ADI) method has been introduced to FDTD to remove that CFL condition. This paper has novelty in quantification of the contribution of the spatial discretisation on error of FD-ADI-FDT and, based on this result, in proposing the scheme to determine the temporal and spatial discretisation from the viewpoint of accuracy