Tadao Ohtani

Phase velocity errors of the nonstandard FDTD method and comparison with other high-accuracy FDTD methods

Several high accuracy finite-difference time-domain (FDTD) methods have been developed to overcome the phase velocity errors present in the FDTD method. The nonstandard FDTD method has been developed as one of those. The phase velocity errors of the method are investigated and the characteristics are compared with other high-accuracy FDTD methods. As a result, the numerical dispersion characteristics of the method are clearly shown and the extremely high-accuracy characteristic at the desired frequency is confirmed.

The nonstandard FDTD method using a complex formulation

In this paper, a complex nonstandard finite-difference time-domain (CNS-FDTD) method is proposed in order to simulate wave propagation in lossy media. To clarify the characteristics of the method, expressions for the numerical propagation constant and the stability condition are derived. It is found that the CNS-FDTD method is much more accurate and stable than the conventional finite-difference time-domain (FDTD) method. The method is applied to the analysis of a fin ferrite electromagnetic wave absorber with a periodic structure.

Accuracy-Adjustable Nonstandard LOD-FDTD Schemes for the Design of Carbon Nanotube Interconnects and Nanocomposite EMC Shields

The precise design of modern carbon nanoscale interconnects and EMC shields is presented in this paper via a nonstandard locally one-dimensional finite-difference time-domain algorithm. A key attribute of the new generalized technique is its frequency-dependent formulation in conjunction with an accuracy-adjustable meshing process to identify regions of smooth field variation and hence seriously reduce dispersion errors. In this way, the high-order unconditionally-stable method remains fully wideband and generates effective dual grids that allow the consistent analysis of complex carbon nanotube interactions with affordable resources. Numerical simulations, studying the performance features of various demanding applications in a wide frequency range, prove the advantages of the proposed schemes.

An Enhanced Total-Field/Scattered-Field Scheme for the 3-D Nonstandard Finite-Difference Time-Domain Method

The nonstandard finite-difference time-domain (NS-FDTD) method exhibits high accuracy at fixed frequencies, and, thus, proves to be a powerful means of the radar cross section analysis of scattering objects with complex shapes and materials. To this aim, significant enhancement can be pursued in its combination with the FDTD total-field/scattered-field (TF/SF) concept. However, the principal implementation characteristics of the latter in the NS-FDTD technique have yet to be elaborately studied, especially for electrically large domains or structures. Hence, in this paper, a new advanced TF/SF scheme for the 3-D NS-FDTD algorithm is developed and fully validated. Numerical results reveal that the proposed method, considering the features of the NS-FDTD operators, is far more efficient and versatile than the original FDTD one.

A 3-D Interlayer-Based FDTD/NS-FDTD Connection Technique Combined With a Stable Subgrid Model for Low-Cost Simulations

An efficient connection scheme for the stable incorporation of several instructive finite-difference time-domain (FDTD) computing models in the non-standard (NS)-FDTD method is proposed in this paper. Based on a straightforward formulation, the novel technique achieves an optimal FDTD/NS-FDTD connection via an interlayer region. Subsequently, the proposed concept is extended to a robust subgrid algorithm for the 3-D NS-FDTD method through the perfectly matched layer condition to decrease the total computational burden. The merits of the combined methodology are numerically validated by diverse applications, such as wire antennas and microwave devices.

Optimal Coefficients of the Spatial Finite Difference Operator for the Complex Nonstandard Finite Difference Time-Domain Method

Optimal coefficients of the spatial finite difference (FD) operator for the complex nonstandard finite difference time-domain (CNS-FDTD) method are presented. To derive the optimal coefficients that minimize the dispersion error, we employ a semianalytical method based on the FD Laplacian. The propagation constant is a complex number in lossy media, therefore, the derivation of the coefficients is more complicated than the derivation for the NS-FDTD method. It is confirmed by numerical tests using the numerical dispersion equation that our coefficients give the CNS-FDTD method a higher accuracy than the standard FDTD method. The coefficients are used for the reflection analysis of a grid ferrite electromagnetic wave absorber, and the validity of the coefficients is shown. The calculation time to derive the coefficients is negligible compared with that for the CNS-FDTD calculations themselves.

Overlap Algorithm for the Nonstandard FDTD Method Using Nonuniform Mesh

In this paper, the overlap algorithm is applied to the nonstandard finite-difference time-domain (NS-FDTD) method using a nonuniform mesh in a 2-D space. The characteristics of the overlap algorithm are numerically examined and compared with a no overlap algorithm. The results show that the reflection rate from the interface of the two meshes using the overlap algorithm is less than -80 dB, which is smaller than that of the NS-FDTD method without the overlap. Consequently, it is shown that the overlap algorithm is more suitable for the NS-FDTD method when using a nonuniform mesh. The overlap algorithm is successfully applied to the analysis of a dielectric flat panel and a corrugated surface

A 4-D Subgrid Scheme for the NS-FDTD Technique Using the CNS-FDTD Algorithm With the Shepard Method and a Gaussian Smoothing Filter

A precise subgrid technique for the nonstandard finite-difference time-domain (NS-FDTD) method in 4-D (i.e., 3-D space and 1-D time) is proposed in this paper. The novel algorithm is efficiently blended with the Shepard scheme and a Gaussian smoothing filter to minimize the error in the interpolated values used for the spatial connection process. Moreover, the required time interpolation is performed via the complex (C)NS-FDTD approach. A key advantage of the proposed formulation is its structural simplicity, due to the prior interpolation concepts and the absence of any nonphysical convention, which enables its straightforward application to a variety of realistic problems. The numerical results validate the benefits of the method by means of different subgrid simulation scenarios.

Characteristics of the Boundary Model in the 2-D NS-FDTD Method

This paper investigates the representation of the dielectric boundary and the absorbing boundary conditions (ABC) that are major concerns in the nonstandard FDTD (NS-FDTD) method. The effective permittivity model of the dielectric boundary is examined and it is found that its accuracy decreases when the boundary coincides with a node. To overcome this difficulty, we propose an alternative, highly accurate boundary model based on an analytic boundary condition. The accuracy of Berengers split-field perfectly matched layer (PML) as an ABC is also demonstrated for the NS-FDTD algorithm.

Efficient suppression of artificial reflections in the TF/SF scheme for the nonstandard FDTD method

A 3-D reflection-reduced total-field/scattered-field (TF/SF) scheme for the accuracy enhancement of the non-standard finite-difference time-domain (NS-FDTD) method is developed in this paper. Based on the properties of the NS-FDTD operators, the new technique can considerably suppress the undesired reflection waves due to the TF/SF separation, compared to the usual FDTD one. Thus, electrically-large problems, such as the computation of aircraft radar cross sections (RCS), can be very precisely analyzed. Numerical outcomes substantiate these advantages and unveil the superiority of the proposed scheme over existing implementations.