When the Laguerre-based finite-difference time-domain (FDTD) method is used for electromagnetic problems, a huge sparse matrix equation results, which is very expensive to solve. We previously introduced an efficient algorithm for implementing an unconditionally stable 2-D Laguerre-based FDTD method. We numerically verified that the efficient algorithm can save CPU time and memory storage greatly while maintaining comparable computational accuracy. This paper presents new efficient algorithm for implementing unconditionally stable 3-D Laguerre-based FDTD method. To do so, a factorization-splitting scheme using two sub-steps is adopted to solve the produced huge sparse matrix equation. For a full update cycle, the presented scheme solves six tri-diagonal matrices for the electric field components and computes three explicit equations for the magnetic field components. A perfectly matched layer absorbing boundary condition is also extended to this approach. In order to demonstrate the accuracy and efficiency of the proposed method, numerical examples are given.

Efficient Implementation for 3-D Laguerre-Based Finite-Difference Time-Domain Method

In the application of two-dimension (2D) finite-difference time-domain (FDTD) to scattering analysis of object embedded in layered media, the incident electromagnetic wave propagation is much more complicated, it can not inject the plane wave source by traditional method. To solve this problem, the Π-shape total-field/scattering- field (TF-SF) boundary scheme is presented. The side TF-SF boundaries are governed by the modified 1D Maxwell's equations, but the discretization for which to p-wave is more difficult than n- wave. Then an auxiliary magnetic variable is used, which can develop the modified 1D-FDTD to p-wave without any approximately. To truncate the modified 1D-FDTD, the convolutional perfectly matched layer (CPML) absorbing boundary condition (ABC) is also given. Examples showthe feasibility and applicability of proposed Π-shape TF/SF boundaries scheme.

/pdf/analysis-of-tf-sf-boundary-for-2d-fdtd-with-plane-p-wave-e4puv4xu56.pdf

Analysis of TF-SF Boundary for 2D-FDTD with Plane P-Wave Propagation in Layered Dispersive and Lossy Media

We previously introduced an efficient algorithm for implementing the 2-D Laguerre-based finite-difference time-domain (FDTD) method. Numerical results indicated that the efficient algorithm can save CPU time and memory storage greatly while maintaining comparable computational accuracy. However, the splitting error associated with the perturbation term becomes pronounced in regions with larger spatial derivatives of the field. In this paper, we present a new efficient algorithm based on the use of an iterative procedure to reduce the splitting error. The new algorithm does not involve any nonphysical intermediate variables, and its update equations are much simpler and more concise than the original ones. Instead of applying the iterative procedure uniformly to the entire computational domain, one can apply an additional number of iterations to regions with relatively large field variation. Using this approach, the overall accuracy can be improved with little computational overhead. Numerical examples are used to illustrate the effectiveness of the proposed algorithm.

A New Efficient Algorithm for the Unconditionally Stable 2-D WLP-FDTD Method

A 3-D total-field/scattered-field (TF/SF) plane-wave source was developed for the analysis of the plane wave propagation characteristics in the reentry plasma sheath. Owing to the dynamic variation in the surrounding flow field, the plasma sheath during the reentry process presents various 3-D inhomogeneous structures, such as dynamic plasma turbulence and considerable metal ablation particles. The proposed 3-D model can be efficiently applied to simulate the scattering effects of the 3-D inhomogeneous structures on the electro-magnetic (EM) signals. The proposed model utilizes a 3-D TF/SF boundary to introduce the plane wave source into the simulation domain, and six pairs of 2-D auxiliary propagators are created to generate the incident field on the TF/SF boundary based on the phase matching and the current density convolution finite-difference time-domain (JEC-FDTD) method. The uniaxial anisotropy perfectly matched layer (UPML) is modified as the absorbing boundary condition of the 2-D propagators. Implementation issues such as stability and dispersion are also discussed. The accuracy and efficiency of the proposed scheme are validated by admirable numerical simulation results and excellent agreement with the transmission line analogy method.

A 3-D Total-Field/Scattered-Field Plane-Wave Source for the FDTD Analysis of Reentry Plasma Sheath

In this paper, an efficient domain decomposition technique is introduced into the unconditionally stable finite-difference time-domain (FDTD) method based on weighted Laguerre polynomials to solve two-dimensional (2-D) electromagnetic scattering problems. The whole computational space is decomposed into multiple subdomains where there is no direct field coupling between any two different subdomains. For the large sparse matrix equation generated by the implicit scheme, the domain decomposition technique transforms this large scale equation into some independent smaller equations. With the total-field/scattered-field boundary and Mur's second-order absorbing boundary condition, the radar cross sections of two 2-D structures are calculated. The numerical examples verify the accuracy and efficiency of the proposed method.

An Efficient Domain Decomposition Laguerre-FDTD Method for Two-Dimensional Scattering Problems

This letter presents an efficient algorithm for the unconditionally stable two-dimensional finite-difference time-domain method with weighted Laguerre polynomials (2-D WLP-FDTD). The huge sparse matrix equation is solved with a factorization-splitting scheme. This leads to much less CPU time and memory storage than those in the conventional implementation. To verify the accuracy and efficiency of the proposed method, two numerical examples are given.

Efficient Implementation for the Unconditionally Stable 2-D WLP-FDTD Method

In this letter, the alternating-direction-implicit (ADI) technique is applied to the body of revolution finite-difference time-domain (BOR-FDTD) method, resulting in an unconditionally stable ADI-BOR-FDTD. It inherits the advantages of both ADI-FDTD and BOR-FDTD methods, i.e., not only eliminating the restraint of the Courant-Friedrich-Lecy condition, with an efficient saving of CPU running time, but also leading to a significant memory reduction in the storage of the field components. To overcome the singularity, a special treatment is made along the vertical axis of the cylindrical coordinates. Numerical results are presented to demonstrate the effectiveness of the proposed algorithm

Unconditionally Stable ADI–BOR–FDTD Algorithm for the Analysis of Rotationally Symmetric Geometries

This letter proposes a total-field/scattered-field (TF/SF) formulation and perfectly matched layer (PML) absorbing boundary condition for the unconditionally stable finite-difference time-domain (FDTD) method based on weighted Laguerre polynomials (WLPs). This approach provides the computational flexibility in electromagnetic scattering and improved performance yet maintains unconditional stable. Numerical results show the TF/SF connecting boundary and PML are effective in the WLP-FDTD method for scattering

TF/SF Boundary and PML–ABC for an Unconditionally Stable FDTD Method

A new two-dimensional (2-D) finite-difference time domain (FDTD) method applied to scattering by infinite objects with oblique incidence is proposed. 2-D Maxwell's equations, differential equations, and perfectly matched layer (PML) absorbing boundary conditions (ABC) are derived. The incident wave, computed by the 1-D FDTD method, is set on the connecting boundary. The accuracy and the efficiency of the proposed method have been verified by comparing the results of the split-field periodic FDTD method, the sine-cosine method, and the transmission line theory method with the proposed method.

A new 2-D FDTD method applied to scattering by infinite objects with oblique incidence

Transient performance of grounding systems is simulated using the finite-difference time-domain (FDTD) method for solving Maxwell's equations. The derivation of the transient current is first adjusted to obtain accurate impedance. Then, the FDTD calculation model is optimized to predict the grounding system impedance accurately without resulting in huge computational resources. From evaluation, the direction parallel to the connecting line is supposed to integrate the transient voltage. The transient voltage should be integrated 20 m in length and the reference electrode to be 30 m from the grounding system, and these lengths should be further enlarged for a large dimension grounding system. The transient impedance of the five lightning current components is very close to each other except the multiple burst, and the current should be injected close to the ground.

FDTD Calculation Model for the Transient Analyses of Grounding Systems

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