3D unconditionally stable FDTD modeling of micromagnetics and electrodynamics

The alternating-direction implicit finite-difference time-domain (ADI-FDTD) method is a promising unconditionally stable scheme that may improve the computational efficiency. However, no general dispersive media were considered in the ADI-FDTD community. The dispersive property, in fact, is important for semiconductor device design at radio-frequency. In this paper, the ADI-FDTD method is applied to complex structures such as on-chip spiral inductor with honeycomb oxide trench, buried layer removal, and radial patterned ground shield. The proposed formula is applicable to linearly dispersive and lossy media. Using this approach, the overall accuracy has been obtained with little computational overhead

The current source implementation for the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method is examined in this letter. By regarding the ADI-FDTD method as an approximate factorization of the Crank-Nicolson scheme, current source is naturally coupled into simulations. As a result, field distribution is much more improved and free of asymmetry.

An efficient and unconditional stable formulations of the perfectly matched layer (PML) are presented for truncating linear Debye and Lorentz dispersive Finite Difference Time Domain (FDTD) grids. The formulations incorporate the Digital Signal Processing algorithms developed for digital filters into the Alternating Direction Implicit FDTD method. Numerical examples are included to validated the proposed formulations.

In this paper, a novel approach is introduced towards an efficient Finite-Difference Time-Domain (FDTD) algorithm by incorporating the Alternating Direction Implicit (ADI) technique to the Nonorthogonal FDTD (NFDTD) method. This scheme can be regarded as an extension of the conventional ADI-FDTD scheme into a generalized curvilinear coordinate system. The improvement on accuracy and the numerical efficiency of the ADI-NFDTD over the conventional nonorthogonal and the ADI-FDTD algorithms is carried out by numerical experiments. The application in the modelling of the Electromagnetic Bandgap (EBG) structure has further demonstrated the advantage of the proposed method.

This paper describes the relaxation technique for the alternating direction implicit finite-difference time-domain (ADI-FDTD) method. The ADI-FDTD method is computationally more complicate than the conventional FDTD and this method requires solving the tridiagonal matrix equation. Thus, this method may require more computational cost than the conventional method due to the large scale tri-diagonal matrix solution corresponding to a large number of meshes. In this paper, relaxation-based solution technique is discussed for the matrix solution and a simple numerical example is shown. As a result, it is confirmed that ADI-FDTD method with the relaxation technique is useful for the electromagnetic field simulation

An one-step arbitrary-order leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is presented. Its unconditional stability is analytically proven and numerically verified. Its numerical properties are shown to be identical to those of the conventional ADI-FDTD and LOD-FDTD methods. However, its computational expenditure is found to be the lowest. In other words, in comparison with the ADI-FDTD and LOD-FDTD methods, the one-step arbitrary-order leap-frog ADI-FDTD method retains identical numerical modeling accuracy but with higher computational efficiency.

A three-dimensional unconditionally-stable locally-one-dimensional finite-difference time-domain (LOD-FDTD) method is proposed and is proved unconditionally stable analytically. In it, the number of equations to be computed is the same as that with the conventional three-dimensional alternating direction implicit FDTD (ADI-FDTD) but with reduced arithmetic operations. The reduction in arithmetic operations leads to approximately 20% less computational time in comparisons with the ADI-FDTD method.

Ground penetrating radar (GPR) forward is one of the geophysical research directions.Through the forward of geological model,the database of radar model can be enriched and the characteristics of typical geological radar echo images can be understood,which in turn can guide the data interpretation of GPR measured profile,thereby improving the GPR data interpretation level.In this article,the interpolating wavelet scale function by using iterative interpolation method is presented,and the derivative of scale function is used in spatial differentiation of discrete Maxwell equations. The forward modeling formula of GPR based on the interpolation wavelet scale method is derived by using fourth-order Runge-Kutta method (RK4) for calculating the higher time derivative.Compared with the conventional finite difference time domain (FDTD) algorithm based on the central difference method,the interpolation wavelet scale algorithm improves the accuracy of GPR wave equation in both space and time discretization.Firstly,the FDTD algorithm and the interpolation wavelet scale method are applied to the forward modeling of a layered model with analytic solution. Single channel radar data and analytical solution fitting indicate that the interpolation wavelet scale method has higher accuracy than FDTD,with the same mesh generation used.Therefore,auxiliary differential equation perfectly matching layer (ADE-PML) boundary condition is used on an interpolation wavelet scale,and the comparisons between reflection errors obtained using CPML (FDTD),RK4ADE-PML (FDTD),and RK4ADE-PML (interpolating wavelet scales) in a homogeneous medium model show that the absorption effect of RK4ADE-PML (interpolating wavelet scales) is better than the other two absorbing boundaries.Finally,interpolation wavelet scale method,with both UPML,FDTD and RK4ADE-PML loaded,is used for two-dimensional GPR forward modeling,showing good absorption effect for evanescent wave.From all the experimental results,the following conclusions are obtained.1) Using the derivative of the interpolating wavelet scale function instead of central difference schemes for the spatial derivative discretization of Maxwell equations and time derivative calculated using the fourth-order Runge Kutta algorithm,the interpolating wavelet scale algorithm has higher accuracy than regular FDTD algorithm due to the improvement in the spatial and time accuracy of GPR wave equation.2) The best absorption layer parameters of interpolating wavelet scale RK4ADE-PML are selected, when the maximum value of the reflection error is the minimum.The maximum reflection error can reach-93 dB,which increases 20 dB compared with that of UMPL boundary in FDTD algorithm.And the higher simulation accuracy of interpolating wavelet scale algorithm than FDTD algorithm is confirmed after calculating single channel radar data.3) Comparing wave field snapshots of GPR forward modeling,radar pictures from wide-angle method and section method indicates that interpolating wavelet scale RK4ADE-PML reduces reflection error of absorption boundary,improves both spatial and time accuracy,is more effective than UPML boundary in eliminating false reflection of large angle incidence, and has better absorption effect for evanescent wave and low-frequency wave.

9 - Computational Electromagnetics: The Finite-Difference Time-Domain Method

Two-dimensional (2D) simulation of a linear induction launcher-type coil gun is performed by the cylindrical finite-difference time domain (FDTD) method. Maxwell's equations in cylindrical coordinates are used to formulate the problem. Circular symmetry is assumed for reducing the 3D problem to a 2D one. A singularity that appeared at r=0 is extracted by using the integral formulation of the FDTD method. A special quasi-static approximation of the FDTD method is applied in the cylindrical problem space which is terminated with the second-order Mur absorbing boundary condition. The armature movement in the FDTD method is treated by the quasi-steady-state method. An experimental model was built, and the muzzle velocity was measured for comparison with the calculated value. Good agreement was obtained.

An efficient higher order alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method for the unconditionally stable analysis of curvilinear electromagnetic compatibility (EMC) applications is presented in this paper. The novel algorithm launches a class of precise spatial/temporal nonstandard forms that drastically suppress the dispersion errors of the ordinary approach as time-step increases and mitigate its strong dependence on cell shape or mesh resolution. For arbitrary interface media distributions that do not follow the grid lines, a convergent transformation based on a rigorous extrapolating practice is introduced. Moreover, infinite domains are successfully treated by optimized higher order curvilinear PMLs. Hence, the proposed technique achieves notable accuracy far beyond the Courant limit, subdues the ADI error mechanisms, and offers serious savings, as verified by the solution of several complex EMC problems.

The finite-difference time domain (FDTD) method is a numerical technique based on the finite difference concept. It is employed to solve Maxwell's equations for the electric and magnetic field distributions in both the time and spatial domains. The FDTD method utilizes the central difference approximation to discretize two of Maxwell's curl equations, namely, Faraday's and Ampere's laws, in both the time and spatial domains, and then solve the resulting equations numerically to derive the electric and magnetic field distributions at each time step and spatial point using the explicit leap-frog scheme. The FDTD solution, thus derived, is second-order accurate, although the difference formulation is first order, and is stable if the time step size is chosen to satisfy the special criterion.

In this paper, transient electromagnetic analysis of rectangular metallic enclosures with apertures illuminated by electromagnetic pulse (EMP) is investigated using alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method. The dispersive property of substrate of printed circuits boards (PCBs) is characterized by the Debye model. Numerical results shows that induced voltage of inner circuits are seriously affected by angle of incidence, polarization and magnitude of the EMP, and length of apertures. Based on the transient response, further design of protection can be implemented to suppress the received jitter of voltage pulses.

For over 100 years after the publication of Maxwell's equations in 1865, essentially all solution techniques for electromagnetic fields and waves were based on Fourier‐domain concepts, assuminga prioria time‐harmonic (sinusoidal steady‐state) field variation and possibly the existence of a particular Green's function or a set of spatial modes. In 1966, Kane Yee's seminal paper introduced a complete paradigm shift in how to solve Maxwell's equations, reporting a field evolution‐in‐time technique that subsequently evolved into the finite‐difference time‐domain (FDTD) method. In the decades since the publication of Yee's paper, there has been an explosion of interest in FDTD and related grid‐based time‐marched solutions of Maxwell's equations among scientists and engineers. During this period, FDTD modeling has evolved to an advanced stage enabling large‐scale simulations of full‐wave time‐domain electromagnetic wave interactions with volumetrically complex structures over large frequency ranges, spatial scales, and timescales. Currently, FDTD modeling spans the electromagnetic spectrum from ultralow frequencies to visible light. FDTD modeling is routinely conducted as an invaluable virtual laboratory bench in scientific inquiry and exploration in electrodynamics; as an integral part of the electromagnetic engineering design and optimization process; and as a powerful forward solver in imaging and sensing inverse problems. This article reviews the technical basis of the key features of FDTD solution techniques for Maxwell's equations and provides 18 modeling examples spanning the electromagnetic spectrum to illustrate the power, flexibility, and robust nature of FDTD computational electrodynamics simulations.

Finite difference time domain (FDTD) is widely used to compute the transient behavior of transmission lines. However, the time step of classic FDTD is limited by the Courant-Friedrich-Lewy (CFL) condition, which makes it not sufficiently efficient for relative low frequency (compared with computation cell size and wave length) signals. The FDTD with alternating direction implicit (ADI) technique is not restricted by the CFL condition, but suffers from numerical dispersions. This paper employs the spectral deferred correction method as the time marching scheme to solve the semidiscretized form of the telegraph equation. The method is unconditionally stable, which allows a larger time step, and can be essentially arbitrary high order accurate.