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PML Implementation for ADI-FDTD in Dispersive Media

Wang Yu,Yuan Nai-chang,
王 禹

电子与信息学报 , 2005,
Abstract: Alternating Direction Implicit-Finite Difference Time Domain(ADI-FDTD) is unconditionally stable and the maximum time step size is not limited by the Courant stability condition, but rather by numerical error. Compared with the conventional FDTD method, the time step size of ADI-FDTD can be enlarged arbitrarily. In this paper 2D PML implementation is proposed for ADI-FDTD in dispersive media using recursive convolution method. ADI-FDTD formulations for dispersive media can be derived from the simplified Perfectly Matched Layer (PML). Numerical results of ADI-FDTD with PML for dispersive media are compared with FDTD. Good agreement is observed.
Unconditionally Stable Leapfrog Adi-FDTD Method for Lossy Media
Theng Huat Gan;Eng Leong Tan
PIER M , 2012, DOI: 10.2528/PIERM12090307
Abstract: This paper presents an unconditionally stable threedimensional (3-D) leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method for lossy media. Conductivity terms of lossy media are incorporated into the leapfrog ADI-FDTD method in an analogous manner as the conventional explicit FDTD method since the leapfrog ADI-FDTD method is a perturbation of the conventional explicit FDTD method. Implementation of the leapfrog ADI-FDTD method for lossy media with special consideration for boundary condition is provided. Numerical results and examples are presented to validate the formulation.
Analysis of the Numerical Dispersion of Higher Order ADI-FDTD

Xu Li-jun,Yuan Nai-chang,

电子与信息学报 , 2005,
Abstract: In this paper, a new higher order Alternating Direction Implicit Finite-Difference Time-Domain (ADI-FDTD) formulation in particular, a second-order-in-time, fourth-order-in-space AD-FDTD method is presented for the first time. At the same time ,the unconditional stability of the higher order ADI-FDTD formulation is analytically proved. By analysis of the amplification factors, the numerical dispersion relation is derived. In addition, the numerical dispersion errors are investigated. Finally numerical results indicate that the higher order ADI-FDTD has s better accuracy compared to the ADI-FDTD method.
Stability and Dispersion Analysis for Three-Dimensional (3-D) Leapfrog Adi-FDTD Method
Theng Huat Gan;Eng Leong Tan
PIER M , 2012, DOI: 10.2528/PIERM11111803
Abstract: Stability and dispersion analysis for the three-dimensional (3-D) leapfrog alternate direction implicit finite difference time domain (ADI-FDTD) method is presented in this paper. The leapfrog ADI-FDTD method is reformulated in the form similar to conventional explicit FDTD method by introducing two auxiliary variables. The auxiliary variables serve as perturbations of the main fields variables. The stability of the leapfrog ADI-FDTD method is analyzed using the Fourier method and the eigenvalues of the Fourier amplification matrix are obtained analytically to prove the unconditional stability of the leapfrog ADI-FDTD method. The dispersion relation of the leapfrog ADI-FDTD method is also presented.
Unified Efficient Fundamental Adi-FDTD Schemes for Lossy Media
Ding Yu Heh;Eng Leong Tan
PIER B , 2011, DOI: 10.2528/PIERB11051801
Abstract: This paper presents the unified efficient fundamental alternating-direction-implicit finite-difference time-domain (ADI-FDTD) schemes for lossy media. The schemes presented include averaging, forward-forward, forward-backward and novel exponential time differencing schemes. Unifications of these schemes in both conventional and efficient fundamental forms of source-incorporated ADI-FDTD are provided. In the latter, they are formulated in the simplest, most concise, most efficient, and most fundamental form of ADI-FDTD. The unified update equations and implementation of the efficient fundamental ADI-FDTD schemes are provided. Such efficient fundamental schemes have substantially less right-hand-side update coefficients and field variables compared to the conventional ADI-FDTD schemes. Thus, they feature higher efficiency with reduced memory indexing and arithmetic operations. Other aspects such as field and parameter memory arrays, perfect electric conductor and perfect magnetic conductor implementations are also discussed. Numerical results in the realm of CPU time saving, asymmetry and numerical errors as well as specific absorption rate (SAR) of human skin are presented.
Energy Identities of ADI-FDTD Method with Periodic Structure  [PDF]
Rengang Shi, Haitian Yang
Applied Mathematics (AM) , 2015, DOI: 10.4236/am.2015.62025
Abstract: In this paper, a new kind of energy identities for the Maxwell equations with periodic boundary conditions is proposed and then proved rigorously by the energy methods. By these identities, several modified energy identities of the ADI-FDTD scheme for the two dimensional (2D) Maxwell equations with the periodic boundary conditions are derived. Also by these identities it is proved that 2D-ADI-FDTD is approximately energy conserved and unconditionally stable in the discrete L2 and H1 norms. Experiments are provided and the numerical results confirm the theoretical analysis on stability and energy conservation.
A Hybrid Method Based on ADI-FDTD and Its Celerity Algorithm

Zhang WeiJun,Yuan NaiChang,Li Yi,Zheng QiuRong,

电子与信息学报 , 2005,
Abstract: The paper presents a hybrid method based on FDTD and ADI-FDTD, introduces a method of weighted average to reduce the reflection caused by two different methods on the boundary, and presents a celerity method for the linear, lossless and isotropic medium. The simulation shows that the method is feasible.
The Adi-FDTD Method Including Lumped Networks Using Piecewise Linear Recursive Convolution Technique
Fen Xia;Qing-Xin Chu;Yong-Dan Kong;Zhi-Yong Kang
PIER M , 2013,
Abstract: The lumped network alternating direction implicit finite difference time domain (LN-ADI-FDTD) technique is proposed as an extension of the conventional ADI-FDTD method in this paper, which allows the lumped networks to be inserted into some ADI-FDTD cells. Based on the piecewise linear recursive convolution (PLRC) technique, the current expression of the loaded place can be obtained. Then, substituting the expression into the ADI-FDTD formulas, the difference equations including an arbitrary linear network are derived. For the sake of showing the validity of the proposed scheme, lumped networks are placed on the microstrip and the voltage across the road is computed by the lumped network finite difference time domain (LN-FDTD) method and LN-ADI-FDTD method, respectively. Moreover, the results are compared with those of obtained by using the circuital simulator ADS. The agreement among all the simulated results is achieved, and the extended ADI-FDTD method has been shown to overcome the Courant-Friedrichs-Lewy (CFL) condition.
Study on acceleration technique for ADI-FDTD algorithm based on GPU

LIU Yu,YUAN Hong-chun,LIANG Zheng,

计算机应用 , 2008,
Abstract: With the advancement of Graphics Processing Unit (GPU) and the creation of its new feature of programmability, it has come possible to transfer some of the processing stages in general numerical algorithms from CPU to GPU in order to accelerate the computation. In this paper, starting from a brief introduction to Alternative Direction Implicit Finite Difference Time Domain (ADI-FDTD) algorithm, detailed introduction and analysis were given to the fundamentals and the key technique of GPU for accelerating ADI-FDTD computation, in combination with the implementation frame of the conjugate gradient method for solving linear equations system on GPU. Finally, some computed examples were presented, and various comparisons were made to prove the efficiency and accuracy of this acceleration approach.
Gpu-Accelerated Fundamental Adi-FDTD with Complex Frequency Shifted Convolutional Perfectly Matched Layer
Wei Choon Tay;Ding Yu Heh;Eng Leong Tan
PIER M , 2010, DOI: 10.2528/PIERM10090605
Abstract: This paper presents the graphics processing unit (GPU) accelerated fundamental alternating-direction-implicit finite-difference time-domain (FADI-FDTD) with complex frequency shifted convolutional perfectly matched layer (CFS-CPML). The compact matrix form of the conventional ADI-FDTD method with CFS-CPML is formulated into FADI-FDTD with its right-hand-sides free of matrix operators, resulting in simpler and more concise update equations. Using Compute Unified Device Architecture (CUDA), the FADI-FDTD with CFS-CPML is further incorporated into the GPU to exploit data parallelism. Numerical results show that a much higher efficiency gain of up to 15 times can be achieved.
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