Nonstandard Finite-difference Time-domain Method Research Articles

A subgridding technique for the complex nonstandard FDTD method

AbstractIn this paper, a subgridding method is proposed for the two‐dimensional Complex Nonstandard FDTD (CNS‐FDTD) method. Taking into account the characteristics of the CNS‐FDTD method, new spatial interpolation, difference operator interpolation, and time interpolation are introduced. In order to demonstrate the usefulness of the proposed subgridding method, it is compared with the cases in which linear interpolation and quadratic interpolation of the conventional method are used for the main grids and local grids. It is found that the present subgridding method is superior to the conventional method in terms of stability and accuracy. Further, in the scattering analysis of a large rectangular cavity loaded with a lossy medium, the present subgridding method demonstrated substantial improvement in computation time and number of grids over CNS‐FDTD calculations with the local grid width over the entire space. As a subgridding method, a connection method is explained in a general case where the spatial division ratio of the main grids and local grids is 1:3. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 87(8): 1–9, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20078

On the duality of electric and magnetic fields using the nonstandard FDTD method

AbstractVerifying the duality of electric and magnetic fields using the nonstandard FDTD method is important for far‐field calculations using the equivalence principle and for the reduction of reflection from boundaries of different size lattices. In this paper, the duality of the fields using this method is confirmed in both physically and numerically. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 148–151, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11310

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.

Numerical dispersion and stability condition of the three‐dimensional nonstandard FDTD method

AbstractIn order to reduce the phase error in FDTD analysis, the NS‐FDTD method has been conceived by Cole. However, numerical dispersion characteristics and stability condition were not presented by Cole; only the definition for cubic meshes was given. In the present paper, the three‐dimensional NS‐FDTD method is extended to rectangular meshes and the numerical dispersion characteristics and stability condition are derived. From the analysis of the stability condition, it is found that the stability condition of the present method is larger than that in the FDTD method. From the analysis of the numerical dispersion characteristics, it is shown that the method has better accuracy than the FDTD method for both cubic and rectangular meshes. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 86(5): 66–76, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.1122

The nonstandard FDTD method for three‐dimensional acoustic analysis and its numerical dispersion and stability condition

AbstractRecently, the present authors have applied the FDTD (Finite‐Difference Time‐Domain) method to acoustic problems. FDTD is one of the finite‐difference methods in the time domain used in electromagnetic problems. However, in this method, phase errors cannot be neglected in a large‐scale propagation analysis such as indoor acoustic propagation and they cause problems in the analysis. In order to reduce the phase error, Cole has invented the NS‐FDTD (Non‐Standard FDTD) method for electromagnetic problems. However, the numerical dispersion and stability condition are not described in Cole's paper. Also, the definition is given only for a cubic lattice. In this paper, an application of the three‐dimensional NS‐FDTD method to acoustic problems is attempted. Further, the method is extended to a rectangular lattice. The numerical dispersion and stability condition of the present method are derived. As a result, it is shown that the present method has much higher accuracy than the FDTD method. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(9): 15–24, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1115

The phase velocity error and stability condition of the three-dimensional nonstandard FDTD method

The nonstandard finite-difference time-domain (NS-FDTD) method, using a rectangular parallelepipeds structured grid, has been proposed to overcome the dispersion and anisotropic errors of the FDTD method. However, the numerical dispersion and the stability condition have not been examined. Furthermore, the method has been defined only in the isotropic grids. This paper investigates the numerical dispersion and the stability condition of the three-dimensional NS-FDTD method for isotropic and nonisotropic grids. The method is compared with the FDTD method. As a result, this method demonstrates highly accurate characteristics and high Courant stability condition.

Numerical Dispersion and Stability Condition of the Nonstandard FDTD Method

AbstractIn order to reduce the phase error in the FDTD analysis, Cole proposed the NS‐FDTD method. However, in the paper by Cole, numerical dispersion characteristics and accurate stability condition were not presented. Also, definition was given only for cubic lattices. In this paper, the NS‐FDTD method is extended to the rectangular lattices and the numerical dispersion characteristic and the stability condition are derived. From the analysis for the stability condition, it is found that the stability condition in the present method is larger than those for the FDTD method and the FDTD(2, 4) method. From the analysis of the dispersion characteristic, it is shown that the present method has much higher accuracy than the FDTD method whether the lattices are cubic or rectangular. An analysis of a waveguide model is carried out in which the NS‐FDTD method and the FDTD method are mixed. © 2001 Scripta Technica, Electron Comm Jpn Pt 2, 85(1): 22–30, 2002

Scattering analysis of large‐scale cavities using the nonstandard FDTD method

AbstractThe nonstandard FDTD method has been proposed for highly accurate numerical analysis of large structures. However, the conventional nonstandard FDTD has been defined only with isotropic grids, and hence the treatment of arbitrary cavity shapes has been severely restricted. In order to remove this restriction in this paper, the nonstandard FDTD method is extended to more general noniso‐tropic grids. First, the FD Laplacian for the nonisotropic grids is newly defined. From the expression for decomposition by the first‐order difference operator, the nonstandard FDTD equations are derived for nonisotropic grids. The physical meaning of the nonstandard FD method used in the nonstandard FDTD method is clarified. Next, by means of the nonstandard FDTD method extended to nonisotropic grids, a scattering analysis of large‐scale cavities is performed and its effectiveness is demonstrated. The results obtained by the nonstandard FDTD method agree well with the measured values, confirming that the nonstandard FDTD method is effective as a highly accurate scattering analysis method for large‐scale cavities. © 2001 Scripta Technica, Electron Comm Jpn Pt 2, 84(12): 8–16, 2001

The influence of boundary conditions on resonant frequencies of cavities in 3-D FDTD algorithm using non-orthogonal co-ordinates

The 3-dimensional finite-difference time-domain method in non-orthogonal co-ordinates (non-standard FDTD) is used to calculate the frequencies of resonators. The numerical boundary conditions of the method are presented. The influences of boundary conditions and discrete meshes on the numerical accuracy are investigated. We present the nonstandard FDTD method using the boundary-orthogonal mesh and equivalent dielectric constant so that the error is reduced from 8.6% to 3.0% for the cylindrical cavity loaded by a dielectric button.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>