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A high-accuracy realization of the yee algorithm using non-standard finite differences

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 1997年第6期45卷 991-996页

作者： Cole, JB Institute for Information Science and Electronics University of Tsukuba Tsukuba Japan

New nonstandard second-order finite differences (FD's) are introduced, which when substituted into the yee algorithm, reduce the solution error by a factor of 10(-4) on a coarse computational grid, Using lambda/h (grid spacings per wavelength) = 8, one achieves the same accuracy as the standard yee algorithm does at lambda/h = 1140, In addition, greater algorithmic stability allows a reduction in the number of iterations needed to solve a problem.

关键词： FDTD nonstandard finite-difference Maxwell's equations yee algorithm

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High-accuracy yee algorithm based on nonstandard finite differences: New developments and verifications

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2002年第9期50卷 1185-1191页

作者： Cole, JB Univ Tsukuba Inst Informat Sci & Elect Tsukuba Ibaraki 3058873 Japan

We previously described a high-accuracy version of the yee algorithm that uses second-order nonstandard finite differences (NSFDs) and demonstrated its accuracy numerically. We now prove that at fixed frequency and grid spacing h, the leading error term is 0 (h(6)) versus 0 (h(2)) for the ordinary yee algorithm with standard finite differences (SFDs). We numerically verify the superior accuracy of the NSFD algorithm by simulating near-field Mie scattering on a coarse grid and comparing with the SFD one and with analytical solutions. We present an updated stability analysis and show that the maximum time step for the NSFD algorithm is 20 % longer than the SFD time step in two dimensions, and 36 % longer in three dimensions. Finally, parameters that were previously given numerically are now analytically defined.

关键词： finite-difference time-domain (FDTD) Mie scattering near field nonstandard finite-difference (NSFD) photonic crystal yee algorithm

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Antenna design using the finite difference time domain method

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IEICE TRANSACTIONS ON COMMUNICATIONS 2005年第5期E88B卷 1774-1789页

作者： Uno, T Tokyo Univ Agr & Technol Fac Engn Koganei Tokyo 1848588 Japan

The finite difference time domain (FDTD) method has been developed in tandem with the progress of computer technology since K. S. yee applied it to the analysis of an electromagnetic problem in 1966. The FDTD method is widely recognized as a powerful computational tool for analyzing electromagnetic problems involving complex geometries, such as antennas, microwave and optical waveguides and interaction between antennas and the human body. The commercial electromagnetic simulators based on the FDTD are also being developed very actively because users are able to trace temporal electromagnetic behaviors and to easily obtain a practical level of accuracy. However, the user must understand the principle of the method in order to use the simulator efficiently. In this paper, the basic concept and the principle of the FDTD method are reviewed for beginners, including graduate course students, rather than specialists in this discipline. Several recent topics concerning electromagnetic and antenna problems are also introduced.

关键词： yee algorithm absorbing boundary antenna electromagnetic field FDTD method

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Numerical Simulation of Electromagnetic Oil Heating Process by integrating The Maxwell Equations and Fourier Transport Model Using FDTD

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IEEE LATIN AMERICA TRANSACTIONS 2015年第7期13卷 2127-2134页

作者： Munoz, E. A. Del Pino, P. Zozaya, A. Inst Espacial Ecuatoriano Quito Ecuador Univ Carabobo Fac Ingn Valencia Venezuela

This paper presents a methodological approach to estimate temperature variations in oil due to electromagnetic power absorption. In order to do this, it have been simulated an oil heating process using the FDTD method for several frequency values. The simulation has been carried out solving the Maxwell equation through the yee algorithm based on finite differences in time domain and the Fourier heat transport model.

关键词： Oil Heating yee algorithm Heat Transport Model FDTD

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High-accuracy FDTD solution of the absorbing wave equation, and conducting Maxwell's equations based on a nonstandard finite-difference model

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2004年第3期52卷 725-729页

作者： Cole, JB Univ Tsukuba Tsukuba Ibaraki 3058573 Japan

We previously introduced high-accuracy finite-difference time-domain (FDTD) algorithms based on nonstandard finite differences (NSFD) to solve the nonabsorbing wave equation and the nonconducting Maxwell equations. We now extend our methodology to the absorbing wave equation and the conducting Maxwell equations. We first derive an exact NSFD model of the one-dimensional wave equation, and extend it to construct high-accuracy FDTD algorithms to solve the absorbing wave equation, and the conducting Maxwell's Equations in two and three dimensions. For grid spacing h, and wavelength lambda, the NSFD solution error is epsilon similar to (h/lambda)(6) compared with (h/lambda)(2) for ordinary FDTD algorithms using second-order central finite-differences. This high accuracy is achieved not by using higher-order finite differences but by exploiting the analytical properties of the decaying-harmonic solution basis functions. Besides higher accuracy, in the NSFD algorithms the maximum time step can be somewhat longer than for the ordinary second-order FDTD algorithms.

关键词： absorbing wave equation conducting Maxwell equations finite-difference time-domain (FDTD) nonstandard finite differences yee algorithm

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Applications of nonstandard finite difference models to computational electromagnetics

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JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS 2003年第12期9卷 1099-1112页

作者： Cole, JB Banerjee, S Univ Tsukuba Tsukuba Ibaraki 3058573 Japan

We introduce an exact nonstandard finite-difference model of the one-dimensional absorbing wave equation, and use it to develop a high accuracy version of the finite-difference time-domain (FDTD) algorithm to solve the absorbing wave equation and the conducting Maxwell's equations in two and three dimensions. For grid spacing h , and wavelength lambda, the solution error of the ordinary FDTD algorithm is epsilon similar to( h / lambda )(2) , because it uses second-order central finite difference approximations. By exploiting the analytical properties of decaying-harmonic solution basis functions in a nonstandard finite difference model we reduce the error to epsilon similar to( h / lambda )(6) without using higher order finite differences. We have verified the accuracy of the algorithms by comparing with analytic solutions of near-field Mie scattering, and have used them to investigate the optical properties of subwavelength conductive diffraction gratings.

关键词： nonstandard finite differences yee algorithm finite-difference time-domain FDTD absorbing wave equation conducting Maxwell equations

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Autonomous motion planning in global dynamic environment using FDTD method

Autonomous motion planning in global dynamic environment usi...

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12th IASTED International Conference on Robotics and Applications (ICRA)

作者： Hussein, Abdullah M. Hamid, A. K. Univ Sharjah Dept Comp Sci Sharjah U Arab Emirates Univ Sharjah Dept Elect & Comp Engn Sharjah U Arab Emirates

ISBN: (纸本)9780889865952

This paper presents a new formulation of the artificial potential approach to the motion planning problem for a mobile robot in a dynamic global environment. To model the potential field, Maxwell's equations are used. The proposed model is extendable to 3D, the time dimension is modeled by default which means it is a suitable model for time-varying environments, and most important it eliminates the "flat-regions" problem. In this work, a pulse of fixed value at a source point generates the potential electric field. The generated electric field is used to find a free path between a start and goal points. Simulation results reflect the validity and the potentials of the proposed model.

关键词： Maxwell equations FTDT yee algorithm robotics motion planning obstacle avoidance

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TVD and ENO Applications to Supersonic Flows in 2D

TVD and ENO Applications to Supersonic Flows in 2D

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International Conference on Mathematics and Computers in Sciences and in Industry (MCSI)

作者： de Goes Maciel, Edisson Savio Pimenta, Amilcar Porto Ferreira, Eduardo Manfredini Mastorakis, Nikos E. Aeronaut Technol Inst ITA Dept Aeronaut Engn Sao Jose Dos Campos SP Brazil Fed Univ Great Dourados UFGD Dept Energy Engn Dourados MS Brazil Tech Univ Sofia Sofia Bulgaria

ISBN: (纸本)9781479943241

In this work, first part of this study, the high resolution numerical schemes of Lax and Wendroff, of yee, Warming and Harten, of yee, and of Harten and Osher are applied to the solution of the Euler and Navier-Stokes equations in two-dimensions. With the exception of the Lax and Wendroff and of the yee schemes, which are symmetrical ones, all others are flux difference splitting algorithms. All schemes are second order accurate in space and first order accurate in time. The Euler and Navier-Stokes equations, written in a conservative and integral form, are solved, according to a finite volume and structured formulations. A spatially variable time step procedure is employed aiming to accelerate the convergence of the numerical schemes to the steady state condition. It has proved excellent gains in terms of convergence acceleration as reported by Maciel. The physical problems of the supersonic shock reflection at the wall and the supersonic flow along a compression corner are solved, in the inviscid case. For the viscous case, the supersonic flow along a compression corner is solved. In the inviscid case, an implicit formulation is employed to marching in time, whereas in the viscous case, a time splitting approach is used. The results have demonstrated that the yee, Warming and Harten algorithm has presented the best solution in the inviscid shock reflection problem;the Harten and Osher algorithm, in its ENO version, and the Lax and Wendroff TVD algorithm, in its Van Leer variant, have yielded the best solutions in the inviscid compression corner problem;and the Lax and Wendroff TVD algorithm, in its Minmod1 variant, has presented the best solution in the viscous compression corner problem.

关键词： Lax and Wendroff algorithm yee, Warming and Harten algorithm yee algorithm Harten and Osher algorithm TVD and ENO flux splitting Euler and Navier-Stokes equations Finite volume Two-dimensions

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Modelování fotonických struktur pomocí metody konečných diferencí v časové oblasti

Modelování fotonických struktur pomocí metody konečnýc...

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作者： Procházka, Pavel Brno University of Technology

Tato bakalářská práce je zaměřena na základní popis metody konečných diferencí v časové oblasti (FDTD, Finite-Difference Time-Domain method), která slouží k numerick&... 详细信息

Tato bakalářská práce je zaměřena na základní popis metody konečných diferencí v časové oblasti (FDTD, Finite-Difference Time-Domain method), která slouží k numerickému řešení Maxwellových rovnic. FDTD je dnes velmi používaná hlavně proto, že během jednoho výpočtu lze získat výsledky v širokém frekvenčním spektru. Práce obsahuje odvození rovnic pro popis této metody a algoritmus výpočtu. Základním úkolem bylo seznámit se s volně dostupným programem Meep, který k těmto výpočtům slouží a pochopit jeho vlastnosti. Většina funkcí Meep je popsána na třech příkladech v druhé části bakalářské práce.

关键词： FDTD fotonické struktury dokonale přizpůsobené vrstvy yeeův algoritmus FDTD photonic structures perfectly matched layers yee algorithm Text

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One-step finite-difference time-domain algorithm to solve the Maxwell equations

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Physical Review E 2003年第5期67卷 056706-056706页

作者： H. De Raedt K. Michielsen J. S. Kole M. T. Figge []Applied Physics–Computational Physics Materials Science Centre University of Groningen Nijenborgh 4 NL-9747 AG Groningen The Netherlands

We present a one-step algorithm to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We compare the results of this algorithm with those obtained from the yee algorithm and from unconditionally stable algorithms. We demonstrate that for a range of applications the one-step algorithm may be orders of magnitude more efficient than multiple time-step, finite-difference time-domain algorithms. We discuss both the virtues and limitations of this one-step approach.

关键词： .Time-Domain Solve Maxwell equations Unconditionally time step Finite-Difference stable algorithms one-step algorithm yee algorithm

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