Alternating Direction Implicit Finite-difference Time-domain Algorithm Research Articles

Modeling GPR Wave Propagation in Complex Underground Structures Using Conformal ADI-FDTD Algorithm

Ground Penetrating Radar (GPR) is a shallow geophysical method for detecting and locating subsurface targets. The GPR image echo characteristics of complex underground structures can be obtained by carrying out GPR forward modeling research. The traditional finite-difference time-domain (FDTD) method has low efficiency and accuracy. The alternating direction implicit FDTD (ADI-FDTD) algorithm surmounts the stability limitations of the traditional FDTD method, making it possible to select a larger time step for higher computational efficiency. For circular underground structures, a pseudowave produced by the ladder approximation method can be corrected using the surface conformal technique. This paper proposes a high-efficiency and high-accuracy GPR forward modeling method that combines the ADI-FDTD algorithm and surface conformal technology. The performance of the conformal ADI-FDTD algorithm is verified by a simple two-layer model. Based on the proposed algorithm, the GPR image features of three complex underground structure models are obtained. Finally, a field experiment is used to support the accuracy and usefulness of the conformal ADI-FDTD algorithm. The numerical simulation results and experimental results show that the conformal ADI-FDTD algorithm reduces the pseudodiffraction wave caused by the ladder approximation method and can significantly improve the computing efficiency for complex underground structure models.

Three-Dimensional Higher Order PML Based on Alternating Direction Implicit Algorithm

Based on the alternating direction implicit finite-difference time-domain (ADI-FDTD) algorithm, a higher order perfectly matched layer (HO-PML) is proposed to solve the problems in a three-dimensional computational domain. The proposed scheme can not only take advantage of the HO-PML for improving the absorbing performance but also has the advantage of the ADI-FDTD algorithm in terms of the unconditional stability. A dielectric resonator antenna example is carried out to validate its effectiveness. The results show that the Courant–Friedrich–Levy limit can be eliminated and the absorbing performance can be further enhanced.

An Error-Reduced ADI-FDTD Algorithm in Debye Media

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.

One-step leapfrog ADI-FDTD method for simulating electromagnetic wave propagation in general dispersive media

The one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is reformulated for simulating general electrically dispersive media. It models material dispersive properties with equivalent polarization currents. These currents are then solved with the auxiliary differential equation (ADE) and then incorporated into the one-step leapfrog ADI-FDTD method. The final equations are presented in the form similar to that of the conventional FDTD method but with second-order perturbation. The adapted method is then applied to characterize (a) electromagnetic wave propagation in a rectangular waveguide loaded with a magnetized plasma slab, (b) transmission coefficient of a plane wave normally incident on a monolayer graphene sheet biased by a magnetostatic field, and (c) surface plasmon polaritons (SPPs) propagation along a monolayer graphene sheet biased by an electrostatic field. The numerical results verify the stability, accuracy and computational efficiency of the proposed one-step leapfrog ADI-FDTD algorithm in comparison with analytical results and the results obtained with the other methods.

Three-Dimensionally Nonorthogonal Alternating-Direction Implicit Finite-Difference Time-Domain Algorithm for the Full-Wave Analysis of Microwave Monolithic Circuit Devices

An alternating-direction implicit finite-difference time-domain (FDTD) algorithm is applied to the full wave analysis of microwave integrated circuit devices. A 3-D multidomain method is developed in nonorthogonal coordinates. Nonorthogonal grids are only used for the anomalistic regions of a complex structure, whereas the standard FDTD lattice is used for the other regions. By using the Jacobian coordinate transformation, curvilinear coordinates can be converted into conventional FDTD format expediently. The perfectly matched layer is used to truncate the boundary. Accurate griddings using the new scheme are obtained, and the complexity of the algorithm is minimal. To illustrate the theory, a sinusoidal plane wave and a Gaussian pulse that propagate through a localized nonorthogonal grid space is used, and the stability of our code is examined. A newly developed compact microstrip bandpass filter is analyzed using the proposed method. The simulated results agree very well with measurements. As compared to other nonorthogonal FDTD (NFDTD) method, the proposed algorithm is much more efficient than other NFDTD counterpart when complex structures are analyzed.

Stability analysis of the extended ADI-FDTD technique including lumped models

The numerical stability of the extended alternating-direction-implicit-finite-difference-time-domain (ADI-FDTD) method including lumped models is analyzed. Three common lumped models are investigated: resistor, capacitor, and inductor, and three different formulations for each model are analyzed: the explicit, semi-implicit and implicit schemes. Analysis results show that the extended ADI-FDTD algorithm is not unconditionally stable in the explicit scheme case, and the stability criterion depends on the value of lumped models, but in the semi-implicit and implicit cases, the algorithm is stable. Finally, two simple microstrip circuits including lumped elements are simulated to demonstrate validity of the theoretical results.

An efficient state‐space ADI‐PML algorithm for truncating DNG metamaterial FDTD domains

AbstractEfficient and unconditionally stable formulations of the anisotropic perfectly matched layer are presented for truncating double negative (DNG) metamaterial finite difference time domain (FDTD) grids. In the proposed formulations, the state‐space equations are employed in the alternating direction implicit FDTD algorithm to obtain update equations for the field equations in the DNG metamaterial domains. Numerical example carried out in one‐dimensional Lorentzian type DNG metamaterial domain is included to show the validity of the proposed formulations. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 494–498, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22162

Analysis of planar circuits using an unconditionally stable 3D 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

Efficient ADI-FDTD/modified matrix pencil method for microwave integrated circuit analysis

This paper presents a new combination of the 3D alternating-direction implicit finite-difference time-domain (ADI-FDTD) method and the modified matrix pencil (MMP) method for the efficient calculation of microwave integrated circuits. It is demonstrated that the time step in the ADI-FDTD algorithm can be four times greater than that of the conventional FDTD without a large loss of accuracy. The MMP method can be used to further reduce the computational time by more than 60% with a reasonable accuracy comparable to that obtained using the ADI-FDTD method in the frequency domain. The iteration number of the ADI-FDTD algorithm combined with the MMP method can be 12 times less than that of the conventional FDTD method for the analysis of microstrip circuits. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 46: 391–395, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20997