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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.
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.
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.
Optimal error estimates and energy conservation identities of the ADI-FDTD scheme on staggered grids for 3D Maxwell's equations  [PDF]
Liping Gao,Bo Zhang
Mathematics , 2011,
Abstract: This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain (ADI-FDTD) method which is a popular scheme for solving the 3D Maxwell equations. Precisely, for the case with a perfectly electric conducting (PEC) boundary condition we establish the optimal second-order error estimates in both space and time in the discrete $H^1$-norm for the ADI-FDTD scheme and prove the approximate divergence preserving property that if the divergence of the initial electric and magnetic fields are zero then the discrete $L^2$-norm of the discrete divergence of the ADI-FDTD solution is approximately zero with the second-order accuracy in both space and time. A key ingredient is two new discrete energy norms which are second-order in time perturbations of two new energy conservation laws for the Maxwell equations introduced in this paper. Furthermore, we prove that, in addition to two known discrete energy identities which are second-order in time perturbations of two known energy conservation laws, the ADI-FDTD scheme also satisfies two new discrete energy identities which are second-order in time perturbations of the two new energy conservation laws. This means that the ADI-FDTD scheme is unconditionally stable under the four discrete energy norms. Experimental results are presented which confirm the theoretical results.
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.
Comparison of Cpml Implementations for the Gpu-Accelerated FDTD Solver
Jukka I. Toivanen;Tomasz P. Stefanski;Niels Kuster;Nicolas Chavannes
PIER M , 2011, DOI: 10.2528/PIERM11061002
Abstract: Three distinctively different implementations of convolutional perfectly matched layer for the FDTD method on CUDA enabled graphics processing units are presented. All implementations store additional variables only inside the convolutional perfectly matched layers, and the computational speeds scale according to the thickness of these layers. The merits of the different approaches are discussed, and a comparison of computational performance is made using complex real-life benchmarks.
Perfectly secure data aggregation via shifted projections  [PDF]
David Fernández-Duque
Computer Science , 2015,
Abstract: We study a general scenario where confidential information is distributed among a group of agents who wish to share it in such a way that the data becomes common knowledge among them but an eavesdropper intercepting their communications would be unable to obtain any of said data. The information is modelled as a deck of cards dealt among the agents, so that after the information is exchanged, all of the communicating agents must know the entire deal, but the eavesdropper must remain ignorant about who holds each card. Valentin Goranko and the author previously set up this scenario as the secure aggregation of distributed information problem and constructed weakly safe protocols, where given any card $c$, the eavesdropper does not know with certainty which agent holds $c$. Here we present a perfectly safe protocol, which does not alter the eavesdropper's perceived probability that any given agent holds $c$. In our protocol, one of the communicating agents holds a larger portion of the cards than the rest, but we show how for infinitely many values of $a$, the number of cards may be chosen so that each of the $m$ agents holds more than $a$ cards and less than $2m^2a$.
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