To radiate electromagnetic energy from a single point of a finite difference time domain (FDTD) grid, there are typically two general classes of electromagnetic wave sources; the soft source which consists of impressing a current, and the hard source which consists of impressing an electric field. The physical meaning of the soft source is well understood and its analytical solution is known, whereas there is no analytical solution for the hard source excitation. Nevertheless, many FDTD works utilize the hard source for its practicality. A novel aspect is that the derivation of a field radiated from the hard source towards the free space is identical to the field radiated from the soft source, provided that a certain relationship holds between the source excitations. This provides us with an analytical solution for the field radiated from the hard source. The assessment of accuracy is then considered for a wide band field radiated from a punctual source into frequency-dependent FDTD Debye media. The quantification of the deviation of the waveform observed in the FDTD space from the analytical solution is demonstrated. The numerical experiments with this quantification show that the waveform observed with the soft source excitation matches the one with the hard source excitation when the minimum wavelength to the spatial discretization ratio is greater than 10. It turns out that the soft source outperforms the hard source when the minimum wavelength relative to the spatial discretization is less than 10 in the case of lossless media. Equivalent accuracy is achievable for both lossless and lossy media even when the minimum wavelength to the spatial discretization ratio is lower than 10 due to the loss tangent which absorbs the spurious frequencies related to the numerical noise.

/pdf/comparison-of-fdtd-hard-source-with-fdtd-soft-source-and-13907gej7i.pdf

Comparison of FDTD Hard Source With FDTD Soft Source and Accuracy Assessment in Debye Media

This paper first describes the phenomenon of Gaussian pulse spread due to numerical dispersion in the finite-difference time-domain (FDTD) method for electromagnetic computation. This effect is undesired, as it reduces the precision with which multipath pulses can be resolved in the time domain. The quantification of the pulse spread is thus useful to evaluate the accuracy of pulsed FDTD simulations. Then, using a linear approximation to the numerical phase delay, a formula to predict the pulse duration is developed. Later, this formula is used to design a Gaussian source that keeps the spread of numerical pulses bounded in wideband FDTD. Finally, the developed model and the approximation are validated via simulations.

On the Design of Pulsed Sources and Spread Compensation in Finite-Difference Time-Domain Electromagnetic Simulations

/pdf/high-speed-computational-modeling-in-the-application-of-uwb-467hi37jlj.pdf

High speed computational modeling in the application of uwb signals

A method is introduced for the optimization of the numerical group velocity in standard finite-difference time-domain (FDTD) electromagnetic simulations. Through this method analytical expressions for the extrema of are presented for the first time, thus also characterizing its anisotropy. The knowledge of these expressions is hence essential for the evaluation of the anisotropy error in FDTD-based electrodynamics simulations of the propagation of wavepackets in 2D and 3D. This can be of assistance, for example, in the design of error-bounded FDTD simulations with pulsed sources at low computational cost.

Characterization of the Numerical Group Velocity in Yee's FDTD Grid

The efficiency of the conventional, explicit finite difference time domain (FDTD)method is constrained by the upper limit on the temporal discretization, imposedby the Courant?Friedrich?Lewy (CFL) stability condition. Therefore, there is agrowing interest in overcoming this limitation by employing unconditionally stableFDTD methods for which time-step and space-step can be independentlychosen. Unconditionally stable Crank Nicolson method has not been widely usedin time domain electromagnetics despite its high accuracy and low anisotropy.There has been no work on the Crank Nicolson FDTD (CN?FDTD) method forfrequency dependent medium.In this thesis a new three-dimensional frequency dependent CN?FDTD (FD?CN?FDTD) method is proposed. Frequency dependency of single?pole Debyematerials is incorporated into the CN?FDTD method by means of an auxiliarydifferential formulation. In order to provide a convenient and straightforwardalgorithm, Mur?s first-order absorbing boundary conditions are used in the FD?CN?FDTD method. Numerical tests validate and confirm that the FD?CN?FDTD method is unconditionally stable beyond the CFL limit.The proposed method yields a sparse system of linear equations which canbe solved by direct or iterative methods, but numerical experiments demonstratethat for large problems of practical importance iterative solvers are to be used.The FD?CN?FDTD sparse matrix is diagonally dominant when the time-stepis near the CFL limit but the diagonal dominance of the matrix deteriorateswith the increase of the time-step, making the solution time longer. Selectionof the matrix solver to handle the FD?CN?FDTD sparse system is crucial tofully harness the advantages of using larger time-step, because the computationalcosts associated with the solver must be kept as low as possible. Two best?knowniterative solvers, Bi-Conjugate Gradient Stabilised (BiCGStab) and GeneralisedMinimal Residual (GMRES), are extensively studied in terms of the number ofiteration requirements for convergence, CPU time and memory requirements.BiCGStab outperforms GMRES in every aspect. Many of these findings do notmatch with the existing literature on frequency?independent CN?FDTD methodand the possible reasons for this are pointed out.The proposed method is coded in Fortran and major implementation techniquesof the serial code as well as its parallel implementation in Open Multi-Processing (OpenMP) are presented. As an application, a simulation model ofthe human body is developed in the FD?CN?FDTD method and numerical simulationof the electromagnetic wave propagation inside the human head is shown.Finally, this thesis presents a new method modifying the frequency dependentalternating direction implicit FDTD (FD?ADI?FDTD) method. Although theADI?FDTD method provides a computationally affordable approximation of theCN?FDTD method, it exhibits a loss of accuracy with respect to the CN-FDTDmethod which may become severe for some practical applications. The modifiedFD?ADI?FDTD method can improve the accuracy of the normal FD?ADI?FDTDmethod without significantly increasing the computational costs.

Unconditionally stable finite difference time domain methods for frequency dependent media

An alternative formulation for a frequency dependent (FD) ADI-FDTD method is proposed, based on an electric flux field D tridiagonal matrix rather than an electric field matrix. The procedure for D source excitation is explained. Results show that the accuracy of the method is unaffected by the inclusion of frequency dependency in the model, compared with FD-FDTD.

Alternative formulation of three dimensional frequency dependent ADI-FDTD method

Temporal discretization for UWB systems in three dimensional alternating - direction implicit finite difference time domain method

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.

Numerical noise introduced by the alternating direction-implicit scheme in FDTD for UWB systems

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

Local velocity calculation for spherical wave UWB signals in 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

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

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