Crank-Nicolson Finite-difference Time-domain Method Research Articles

Explicit FDTD method based on iterated Crank–Nicolson scheme

An implicit Crank–Nicolson procedure can be replaced with an explicit iteration process. An explicit finite-difference time-domain method based on the iterated Crank–Nicolson scheme that has been widely used for solving Einstein's equations is newly developed. The formulation is presented with two iterations and its stability condition is also derived. Numerical results are found to agree well with those obtained from the traditional explicit finite-difference time-domain method, showing the validity of the present iterated Crank–Nicolson–finite-difference time-domain method.

Reply to Comments on “Direct-Splitting-Based CN-FDTD for Modeling 2D Material Nanostructure Problems”

In this response letter, we focus on addressing Yu Hang Yang's comments so that the correctness and validity of the proposed auxiliary-differential-equation-based (ADE) Crank-Nicolson finite-difference time-domain method with direct-splitting technique (CNDS-FDTD) are demonstrated. Moreover, related applications in modeling 2D material nanostructure problems are shown.

Unconditionally stable higher order perfectly matched layer applied to terminate anisotropic magnetized plasma

An effective and efficient absorbing boundary condition applied to terminate anisotropic magnetized plasma is proposed in this article. As its mathematical derivations are based on the high order perfectly matched layer (HO-PML) and Crank-Nicolson finite-difference time-domain method, it has the advantages of reducing late-time reflections, attenuating evanescent waves, absorbing low-frequency propagation waves and overcoming the Courant-Friedrichs-Levy condition. To validate the efficiency and effectiveness of the proposed HO-PML, a ridge waveguide model composed of vacuum and the anisotropic magnetized plasma, a dielectric waveguide model composed of the dielectric and the anisotropic magnetized plasma are employed. The numerical results show that the proposal can not only maintain the stability of the algorithm with the increment of the time step but also further enhance the absorbing performance.

Subgridding Boundary Conditions to Model Arbitrarily Dispersive Thin Planar Materials

In a previous work, we presented a hybrid implicit–explicit Crank–Nicolson finite-difference time-domain method for treating multilayered lossy thin slabs. The main advantage of this method was its capability to overcome certain late-time stability issues of the conventional surface impedance boundary condition approaches. In this communication, we extend this method to deal with thin slabs having arbitrarily dispersive profiles. This approach is validated with the analysis of a spherical shell made of a metallic wire mesh whose macroscopic equivalent constitutive parameters are derived from its microscopic structure. The results for the electric field inside the sphere are compared against the analytical data and show good agreement with them.

Corrections to “Linear Analysis of High-Frequency Field-Effect Transistors Using the CN-FDTD Method” [Jun 17 1946-1954

In the above-cited paper [1] , the Crank–Nicolson finite-difference time-domain method is used for the analysis of a high-frequency field-effect transistor (FET). However, two references are missed. In addition, there are some errors in (6b), Fig. 2 , and Table I . The reference of Figs. 1 and 2 is [2] . The reference of Table I is [3] . In (6b), $L_{\mathrm {dd}}$ , $L_{\mathrm {gg}}$ , $L_{\mathrm {ss}}$ , $M_{\mathrm {gd}}$ , and $G_{m}$ should be, respectively, $L_{\mathrm {d}}$ , $L_{\mathrm {g}}$ , $L_{\mathrm {s}}$ , $M_{\mathrm {dg}}$ , and $g_{m}$ . The corrected version of Fig. 2 is depicted here, wherein the designations are consistent with the present correction. The corrected table is also reported here, subsequently, wherein the values are valid when the transistor is biased at $V_{\mathrm {ds}} = 3$ V and $I_{\mathrm {ds}} = 10$ mA.

Linear Analysis of High-Frequency Field-Effect Transistors Using the CN-FDTD Method

The Crank–Nicolson finite-difference time-domain (CN-FDTD) method is used for the linear analysis of a field-effect transistor (FET) based on the distributed model, wherein the FET is considered as an active multiconductor transmission line (AMCTL). The telegrapher’s equations governing the AMCTL are derived and discretized by the CN-FDTD method. The results are compared with measurements and the leapfrog (LF)-FDTD method. Unconditional stability of the CN scheme is investigated. Agreement with measured results is preserved in an acceptable level even by increasing the time step-size by a factor of 1500 to that of the LF-FDTD method.

Application of the Crank–Nicolson FDTD method for analysis of a wideband multi-section hybrid coupler

In this paper the Crank---Nicolson (CN) finite-difference time-domain (FDTD) method is applied for the analysis of a planar wideband hybrid coupler. The proposed method is applied for analysis of transmission lines. Stability issue is investigated for different cases, including lossless and lossy transmission lines. Sufficient conditions for unconditional stability are derived. As a practical problem, a wideband compact hybrid coupler working on 1---6 GHz frequency band is analyzed using the CN-FDTD method. Measurement results show that the proposed coupler provides coupling of 3 ± 0.8 dB with 90° ± 0.85° phase shift and demonstrate the return loss and isolation better than 16 dB over 1---6 GHz. To validate the accuracy of the method, the results of this scheme are compared with measurements and the conditional stable leap-frog (LF) FDTD method. It is observed that using the CN-FDTD, the temporal step-size can be increased up to 1500 time compared with the LF-FDTD method with still good agreement with the measured results.

Extend two-step preconditioning technique for the Crank-Nicolson finite-difference time-domain method to analyze the 3D microwave circuits

The increase of the time-step size significantly deteriorates the property of the coefficient matrix generated from the Crank–Nicolson finite-difference time-domain method. As a result, the convergence of classical iterative methods, such as generalized minimal residual method (GMRES) would be substantially slowed down. The main purpose of this article is to show that the two-step preconditioner can greatly accelerate the convergence of the iterative method, such as GMRES. Numerical simulations show that this two-step preconditioned GMRES iterative method has a faster convergence speed than those methods when the preconditioner is used alone. © 2009 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.

Unconditionally stable Crank–Nicolson finite-different time-domain method for simulation of three-dimensional microwave circuits

An unconditionally stable Crank–Nicolson finite-difference time-domain (CN-FDTD) algorithm is presented for three-dimensional microwave circuit analysis. First, Mur's first–order absorbing boundary condition is applied this CN-FDTD algorithm. A symmetric successive over relaxation–preconditioned biconjugate-gradient algorithm is also proposed to solve the large sparse matrix equation obtained in the CN-FDTD method. Resonant cavity and several planar microstrip circuits are presented to illustrate the versatility of this technique. Numerical results indicate that with a time-step size excessively larger than the Courant–Friedrich–Levy limit, the accuracy of CN-FDTD is still much higher than that of the alternating-direction implicit FDTD.

The unconditionally stable Crank Nicolson FDTD method for three-dimensional Maxwell's equations

In this paper, an accurate and computationally implicit 3D finite-difference time-domain (FDTD) method based on the unconditionally stable Crank–Nicolson scheme (3D CN-FDTD) is presented. The source excitation in 3D CN-FDTD is described and the numerical simulation of the 3D CN-FDTD method is demonstrated through numerical examples. The results of this method, the ADI-FDTD method, and traditional FDTD schemes are compared. A good agreement is obtained for the 3D CN-FDTD method with time steps greatly more than the Courant–Friedrich–Levy (CFL) limit and the traditional Yee FDTD method. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1619–1622, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21684