The Simplest V-Cycle Fast Adaptive Composite Grid ADI-FDTD Method for Two-Dimensional Electromagnetic Simulations

The alternating direction implicit finite-difference time-domain (ADI-FDTD) method is an unconditionally stable numerical scheme, being proposed to remove stability limitations in conventional FDTD methods. Though the computation efficiency has been improved by ADI-FDTD, significant errors have been observed at large time steps. By compensating truncation errors, a low error ADI-FDTD method in Debye media is proposed based the ER(error reduced)-ADI-FDTD, complete three dimensional equations are derived. Simulation results are anlalyzed and compared with existing methods.

With the rapid development of Bluetooth wireless communication, it's highlighted now to applying micro-electro-mechanical systems (MEMS) technique in the radio frequency (RF) field to manufacture broadband Bluetooth antennas. The 10 dB bandwidth and efficiency of the micromachined Bluetooth antenna designed in this paper are more than 11% and 68% respectively; the length is less than 1/10 wavelength. The alternating direction implicit finite-difference time-domain (ADI-KDTD) method for a full three-dimensional (3-D) wave presented is used for modeling and analyzing the micromachine antenna for the first time. Numerical simulation results are compared to those using the conventional 3D finite-difference time-domain (FDTD) method. It is more efficient than the conventional 3-D FDTD method in terms of the central processing unit time if the size of the local minimum cell in the computational domain is much smaller than the other cells and the wavelength.

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

This paper presents unconditionally stable and conformal FDTD schemes which are based on the alternating-direction implicit finite difference time domain (ADI-FDTD) method for accurate modeling of perfectly electric conducting (PEC) objects. The proposed schemes are formulated within the framework of the matrix-vector notation of the finite integration technique (FIT), which allows a systematic and consistent extension of finite difference solution of Maxwell's equations on dual grids. As possible choices of second-order convergent conformal method, we apply the partially filled cell (PFC) and the uniformly stable conformal (USC) schemes for the ADI-FDTD method. The unconditional stability and the rates of convergence of the proposed conformal ADI-FDTD (CADI-FDTD) schemes are verified by means of numerical examples of waveguide problems.

We present a parallel implementation of the three‐dimensional alternating direction implicit finite‐difference time‐domain (ADI‐FDTD) method in Cartesian coordinates using the message passing interface (MPI) library. Parallel implementations not only speed up computations but also increase the maximum solvable problem size. The application of the ADI scheme results in freeing the time‐step size from the Courant‐Friedrichs‐Lewy stability constraint. We demonstrate a speedup of the ADI‐FDTD method through parallelization, even though the communication overhead between the processors is proportional to the volume of the domain, rather than just the surface area of the subdomains as for standard parallel FDTD. We benchmarked our code on an IBM p690 symmetric multiprocessor and also a distributed memory computer cluster with a high‐bandwidth Infiniband interconnect. In both cases, satisfactory scalability and efficiency was demonstrated for simulation domains comprising up to 8 billion mesh cells. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1298–1304, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24310

This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain (ADI-FDTD) method which is a popular scheme for solving the 3D Maxwell’s equations. Precisely, for the case with a perfectly electric conducting (PEC) boundary condition we establish the optimal second-order error estimates in both space and time in the discrete H1-norm for the ADI-FDTD scheme, and prove the approximate divergence preserving property that if the divergence of the initial electric and magnetic fields are zero, then the discrete L2-norm of the discrete divergence of the ADI-FDTD solution is approximately zero with the second-order accuracy in both space and time. The key ingredient is two new discrete modified energy norms which are second-order in time perturbations of two new energy conservation laws for the Maxwell’s equations introduced in this paper. Furthermore, we prove that, in addition to two known discrete modified energy identities which are second-order in time perturbations of two known energy conservation laws, the ADI-FDTD scheme also satisfies two new discrete modified energy identities which are second-order in time perturbations of the two new energy conservation laws. This means that the ADI-FDTD scheme is unconditionally stable under the four discrete modified energy norms. Experimental results which confirm the theoretical results are presented.

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.

This paper introduces an unconditionally stable alternating-direction implicit finite-difference time-domain (ADI-FDTD) method enhanced with thin-wire and thin-slot models for efficient simulation of shielded enclosures containing multiscale structures, such as thin wires and thin slots. Conventional FDTD methods face two major challenges in this context: first, the spatial scales of thin wires and slots necessitate excessively fine meshing, and second, the explicit method is bound by the Courant-Friedrichs-Lewy (CFL) stability condition. These limitations collectively result in prohibitive computational costs. Our proposed approach overcomes these hurdles by integrating the unconditionally stable ADI-FDTD scheme with dedicated thin-wire and thin-slot representation models. Detailed iterative formulations are derived, and the unconditional stability of the proposed method is rigorously demonstrated. Numerical examples confirm that our method achieves comparable accuracy at a substantially reduced computational burden over the traditional FDTD approach. Finally, we demonstrate that this hybrid algorithm enables high-precision analysis of the shielding effectiveness (SE) of metallic enclosures under arbitrary wave incidence with markedly improved efficiency.

A three-dimensional unconditionally stable five-step locally one-dimensional finite-difference time-domain (LOD-FDTD) method is presented. Unlike the two-step LOD-FDTD and three-step LOD-FDTD methods, the proposed method has second order temporal accuracy. Hence, it gives less numerical dispersion than the two-step LOD-FDTD and three-step LOD-FDTD methods. It also gives less numerical dispersion than the alternating direction implicit finite-difference time-domain (ADI-FDTD) method. Moreover, for every propagation angle θ, it provides very small anisotropy error than the above-mentioned FDTD methods. Effects of the time step and the mesh size on the performance of the proposed method are discussed in detail. In this paper, validation of the stability and the accuracy of the proposed method is done with the help of simulation results. To further show the advantage of the proposed method, performance of the proposed method with artificial coefficients (control parameters) is also discussed in this paper.

This paper presents the implementation of split-field perfectly matched layer (PML) for the efficient fundamental scheme of alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method. The split-field PML is formulated into the ADI generalized splitting formulae cast into matrix-operator-free right-hand sides. The efficient fundamental ADIFDTD with PML incorporated is compared and validated with the conventional ADI-FDTD implementation through numerical simulation. It is found that their reflection errors are identical which confirm that both implementations are equivalently effective. On the other hand, by comparing their CPU time, it is ascertained that substantial gain in the overall efficiency may be achieved for the efficient fundamental scheme.

In this letter, the current source implementations are presented for the hybrid implicit–explicit finite-difference time-domain (HIE-FDTD), the improved HIE-FDTD, and the leapfrog HIE-FDTD methods. The asymmetry and the field errors of these HIE-FDTD methods are investigated for all possible values of the time index parameters. The proposed implementations give very low asymmetry and field errors for all the three HIE–FDTD methods. The field errors given by these HIE-FDTD methods are lower than those given by the alternating direction implicit finite-difference time-domain (ADI-FDTD) method.

In this paper, a 3D alternating-direction implicit finite-difference time-domain (ADI-FDTD) algorithm is used to analyze planar circuits. The source excitation in ADI-FDTD is described and two kinds of absorbing boundary conditions (ABCs) are jointly employed for ADI-FDTD algorithm: the Gedney's uniaxial PML scheme is applied in the propagation direction, and Mur's 1st-order absorbing boundary condition (ABC) is set on the other outer surfaces. Both time-domain waveforms and S-parameters are presented. The numerical simulations of several examples show that the number of iterations with this ADI-FDTD algorithm can be six times less than that with the conventional FDTD without a large loss of accuracy. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 46: 175–179, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20936

A second-order in time and fourth-order in space, alternating direction implicit finite difference time domain (ADI-FDTD) scheme is presented for radio-wave propagation in a isotropic collisionless plasma. At the same time, the unconditional stability of the higher order ADI-FDTD formulation for plasma is analytically proved. By analysis of the growth factor, the numerical dispersion relation is derived. In addition, the numerical dispersion errors are investigated. From the error analysis and phase velocity data, it is argued that the proposed approach will significantly minimize the dispersion errors compared to the ADI-FDTD method.

A novel global FDTD scheme based on drift-diffuse model of semiconductor combined alternating direction implicit finite-difference time-domain (ADI-FDTD) method is presented. Although it is some complicated, the proposed method can reduce computation time by increasing time increment. Main features of the method are demonstrated by simulation of a distributed diode switch.

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> An arbitrary-order unconditionally stable three-dimensional (3-D) locally-one- dimensional finite-difference time-method (FDTD) (LOD-FDTD) method is proposed. Theoretical proof and numerical verification of the unconditional stability are shown and numerical dispersion is derived analytically. Effects of discretization parameters on the numerical dispersion errors are studied comprehensively. It is found that the second-order LOD-FDTD has the same level of numerical dispersion error as that of the unconditionally stable alternating direction implicit finite-difference time-domain (ADI-FDTD) method and other LOD-FDTD methods but with higher computational efficiency. To reduce the dispersion errors, either a higher-order LOD-FDTD method or a denser grid can be applied, but the choice has to be carefully made in order to achieve best trade-off between the accuracy and computational efficiency. The work presented in this paper lays the foundations and guidelines for practical uses of the LOD method including the potential mixed-order LOD-FDTD methods. </para>