Yan-Tao Duan

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

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 the Unconditionally Stable 2-D WLP-FDTD Method

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.

A New Efficient Algorithm for 3-D Laguerre-Based Finite-Difference Time-Domain Method

We previously introduced a new efficient algorithm for implementing the 2-D Laguerre-based finite-difference time-domain (FDTD) method. The new 2-D efficient algorithm is based on the use of an iterative procedure to reduce the splitting error associated with the perturbation term, and it does not involve any nonphysical intermediate variables. Numerical results indicated that the new efficient algorithm shows better performance for modeling some regions with larger spatial derivatives of the field. In this paper, we extend this approach to a full 3-D wave. Numerical formulations of the new 3-D Laguerre-based FDTD method are devised and simulation results are compared to those using the conventional 3-D FDTD method and the alternating-direction implicit (ADI) FDTD method. We numerically verify that, at the comparable accuracy, the efficiency of the proposed method with an iterative procedure is superior to the FDTD method and the ADI -FDTD method. Also, in order to verify the stability of the iterative procedure, we present a convergence analysis and a long-time simulation to it in the paper.

A New Iterative Algorithm for Efficient 3-D Laguerre-Based FDTD Method

This letter presents a new iterative algorithm for efficient 3-D Laguerre-based finite-difference time-domain (FDTD) method. A new perturbation term and the Gauss-Seidel method are introduced in the algorithm. The theoretical analysis in the frequency domain shows that the splitting error introduced by the new perturbation term grows slower than that of the original one at the high frequency range. The Gauss-Seidel iterative method is used in the iterative procedure to speed up the convergence further. Numerical results show that the new iterative algorithm achieves a comparable accuracy with three iterations comparing to the original one with eight iterations, and the whole CPU time is reduced to about 34.5% of the original one.

PML Absorbing Boundary Condition for Efficient 2-D WLP-FDTD Method

In this letter, Berengers perfectly matched layer (PML) absorbing boundary condition is presented for the efficient two-dimensional (2-D) finite-difference time-domain (FDTD) method with weighted Laguerre polynomials. Through adding a perturbation term, the huge sparse matrix equation is solved with a factorization-splitting scheme. To verify the validity of the proposed formulations, a numerical example of scattering from a 2-D rectangular conductor is given.

Efficient 3-D Laguerre-Based FDTD Method Using a New Temporal Basis

Due to the finite expanding order in an actual numerical simulation, the finite-difference time-domain method based on weighted Laguerre polynomials (Laguerre-FDTD) often has a large error near t=0. In this communication, a new temporal basis is proposed to solve this problem, which is composed of three weighted Laguerre polynomials in adjacent orders. Based on this new temporal basis, the matrix equation for three-dimensional (3-D) FDTD method is derived in which the accumulation term is eliminated. By introducing a perturbation term and an iterative procedure to the matrix equation, an efficient 3-D FDTD method is obtained. To verify the accuracy and efficiency of the proposed FDTD method, two structures are calculated as examples. Numerical results show that the solution of the proposed method has no error at t=0 and the efficiency of the proposed method is superior to the conventional FDTD method, the alternating direction implicit (ADI) FDTD method, and the original efficient Laguerre-FDTD method using a single Laguerre polynomial at a comparable accuracy.

PML ABC for Efficient 3-D Laguerre-based FDTD Method Using a new Perturbation Term

In this letter, the three-dimentional Berengers perfectly matched layer (PML) implementation is proposed for the efficient Laguerre-based finite-difference time-domain method using a new perturbation term. By using this new term and the factorization-splitting scheme, the huge matrix equation of Berengers PML implementation is split into six tridiagonal matrices and solved efficiently. In the numerical validation, the absorbing performance of the proposed PML implementation is studied as a function of the constitutive parameters and is compared to the existing absorbing boundary conditions (ABCs). Numerical results show that the proposed PML implementation has a better absorbing performance.

An Efficient Laguerre-Based BOR-FDTD Method Using Gauss–Seidel Procedure

In this paper, an efficient Laguerre-based body of revolution finite-difference time-domain (BOR-FDTD) method is proposed. A perturbation term and the Gauss-Seidel method are introduced to get the new algorithm. The splitting error caused by the perturbation term can be reduced to a low level by using the iterative method. To be different from its counterpart in the Cartesian coordinate system, the perturbation term used for the off-axis field is not applicable to the field on the axis in the proposed method. On the axis, it is not necessary to add the perturbation term and no nonphysical intermediate variable is involved. No splitting error compensatory term is used for the field on the axis during the iteration. Another difference is that the perturbation term in the proposed method causes a pronounced splitting error on the field point which is close to the axis. Several local iterations near the axis are needed since the splitting error near the axis is especially large. To validate the proposed method, two numerical examples are given. Numerical results show that it obtains a good convergence. Meanwhile, the comparison of the computational expenditure between the proposed method and several other methods indicates its performance.

Numerical dispersion analysis for efficient 2-D Laguerre-based FDTD method

This paper presents the numerical dispersion analysis of the efficient two-dimensional Laguerre-based finite-difference time-domain (FDTD) method. The numerical dispersion relation is derived and the numerical dispersion errors are investigated. The results indicate that, by choosing the suitable values of the sampling point density in space domain and the time-scale factor, one can ensure the numerical dispersion error within certain accuracy.

Calibration schemes for lightning E-dot sensors

A wideband active E-dot sensor is designed and tested in calibration. Thereafter, calibration schemes for E-dot sensor including magnitudes and risetimes are proposed and conducted. Two magnitude calibration methods are performed. Experimental results exhibit that the magnitude calibration coefficients between the two methods are less than 3%, and the 10%-90% risetime of the sensor is less than 7ns, which is well suited for lightning observations. Subtle discrepancy exists between the reference signal and the measured one. These differences are in good agrreement with previous observations, which indicate that dE/dt usually reflect more higher frequency components, and the integration of dE/dt to derive E-field is valid only in the fast rising portion of dE/dt waveforms.