Stable FDTD Method Research Articles

An unconditionally stable FDTD method based on wave equation

AbstractAn unconditionally stable finite‐difference time‐domain (US‐FDTD) method based on wave equation is introduced by making use of Laguerre polynomials as basis functions for expanding field components in time. This new wave‐equation‐based FDTD scheme is not only unconditionally stable but also requires less memory usage. Comparisons among the traditional FDTD, the conventional Laguerre‐polynomial US‐FDTD, and this proposed scheme are presented in the numerical examples in terms of the memory usage and computational time. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 529–532, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24101

Fourth-Order Locally One-Dimensional FDTD Method

A fourth-order two-dimensional (2-D) locally one-dimensional finite-difference time-domain (LOD-FDTD) method is introduced. The numerical dispersion error of this new approach is studied by comparison to the original second-order method. This new approach is proved to be an unconditionally stable FDTD method with improved numerical dispersion.

Perfectly matched layer for two‐dimensional unconditionally stable FDTD method based on approximate Crank‐Nicolson scheme

AbstractA perfectly matched layer (PML) is constructed for two‐dimensional (2D) unconditionally stable (US) FDTD method based on an approximate Crank‐Nicolson scheme. This novel PML preserves unconditional stability of the 2D US‐FDTD method and has very good absorbing performance. Numerical results are included to illustrate effectiveness and performance of this new PML. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1178–1182, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22364

3-D FDTD method with weakly conditional stability

A novel 3-D FDTD method with weakly conditional stability is presented. The time step in this method is only determined by one space discretisation. Compared with the ADI-FDTD method, this method has better accuracy and higher computation efficiency. CPU time for this weakly conditionally stable FDTD method can be reduced to about 3/4 of that for the ADI-FDTD scheme.

Error between unconditionally stable FDTD methods and conventional FDTD method

Both the ADI-FDTD method and the CN-FDTD method can be viewed as approximate factorisation of the conventional FDTD scheme, so the error between these methods and the conventional FDTD method is obtained. It is shown that the error is associated with the time step size, the permittivity and the permeability of the medium, and the spatial variation rate of field. The space discretisation has no relation with the error, which is demonstrated by numerical examples.

A Compact Unconditionally Stable FDTD Method

A novel compact unconditionally stable finite-difference time-domain (US-FDTD) method is introduced. This method utilizes proper intermediate field components to simplify the original unconditionally stable Crank-Nicolson (CN) scheme. The unconditionally stability of the proposed compact US-FDTD method is analytically proven. Numerical results are included to illustrate the stability, accuracy, and efficiency of the proposed compact US-FDTD

Accurate And Computationally Efficient Two-dimensionalUnconditionally Stable FDTD Method

In this paper, an accurate and computationally efficient two-dimensional unconditionally stable finite-difference time-domain (2-D US-FDTD) method based on the Crank-Nicolson scheme is proposed. In particular, in the proposed 2-D USFDTD method the field components are defined at only two time steps n and n+l ; and the original time-dependent Maxwell's equations of the Crank-Nicolson scheme are solved by introducing a proper intermediate value for a field component. Compared to the ADI-FDTD method, the US-FDTD method offers the following two advantages: i) the left-hand and right-hand sides of the original updating equations are balanced (in respect of time step) as much accurate as possible and, ii) only a single iteration that requires less number of updating equations is needed for the field development. The numerical performance of the proposed US-FDTD method over the ADI-FDTD algorithm is demonstrated through numerical examples.

A novel implementation for two‐dimensional unconditionally stable FDTD method

AbstractIn this paper, a novel two‐dimensional unconditionally stable finite‐difference time‐domain (2D US‐FDTD) method based on the Crank–Nicolson (CN) scheme is proposed. In particular, in the proposed 2D US‐FDTD method the field components are defined at only two time steps n and n + 1; and the original time‐dependent Maxwell's equations of the Crank–Nicolson scheme are solved by introducing a proper intermediate value for a field component. Compared to the ADI‐FDTD method, the US‐FDTD method offers the following two advantages: (i) the left‐hand and right‐hand sides of the original updating equations are balanced (with regards to time steps) as accurately as possible and (ii) only a single iteration that requires fewer updating equations is needed for the field development. The numerical performance of the proposed US‐FDTD method over the ADI‐FDTD algorithm is demonstrated through numerical examples. In particular, it is shown that the asymmetric effect (that is, the asymmetric result is obtained even for exactly symmetric computational setups), which always appears in the ADI‐FDTD algorithm, is not observed in the US‐FDTD method. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 38: 457–462, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11089

More accurate and efficient unconditionally stable FDTD method

A more accurate and efficient unconditionally stable finite-difference time-domain (US-FDTD) method is proposed. The two key points of the proposed US-FDTD method are: defining the field components at only n and (n+1) time steps; and arranging the left and right hands of the original updating equations to be as accurate (in respect of time) as possible. It is demonstrated that the US-FDTD method is more efficient (in both computer memory and CUP time) and more accurate than the recently developed ADI-FDTD method.