Book•
Computational Electrodynamics: The Finite-Difference Time-Domain Method
31 May 1995-
TL;DR: This paper presents background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology, and the proposed three-dimensional Yee algorithm for solving these equations.
Abstract: Part 1 Reinventing electromagnetics: background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology. Part 2 The one-dimensional scalar wave equation: propagating wave solutions finite-difference approximation of the scalar wave equation dispersion relations for the one-dimensional wave equation numerical group velocity numerical stability. Part 3 Introduction to Maxwell's equations and the Yee algorithm: Maxwell's equations in three dimensions reduction to two dimensions equivalence to the wave equation in one dimension. Part 4 Numerical stability: TM mode time eigenvalue problem space eigenvalue problem extension to the full three-dimensional Yee algorithm. Part 5 Numerical dispersion: comparison with the ideal dispersion case reduction to the ideal dispersion case for special grid conditions dispersion-optimized basic Yee algorithm dispersion-optimized Yee algorithm with fourth-order accurate spatial differences. Part 6 Incident wave source conditions for free space and waveguides: requirements for the plane wave source condition the hard source total-field/scattered field formulation pure scattered field formulation choice of incident plane wave formulation. Part 7 Absorbing boundary conditions for free space and waveguides: Bayliss-Turkel scattered-wave annihilating operators Engquist-Majda one-way wave equations Higdon operator Liao extrapolation Mei-Fang superabsorption Berenger perfectly-matched layer (PML) absorbing boundary conditions for waveguides. Part 8 Near-to-far field transformation: obtaining phasor quantities via discrete fourier transformation surface equivalence theorem extension to three dimensions phasor domain. Part 9 Dispersive, nonlinear, and gain materials: linear isotropic case recursive convolution method linear gyrontropic case linear isotropic case auxiliary differential equation method, Lorentz gain media. Part 10 Local subcell models of the fine geometrical features: basis of contour-path FD-TD modelling the simplest contour-path subcell models the thin wire conformal modelling of curved surfaces the thin material sheet relativistic motion of PEC boundaries. Part 11 Explicit time-domain solution of Maxwell's equations using non-orthogonal and unstructured grids, Stephen Gedney and Faiza Lansing: nonuniform, orthogonal grids globally orthogonal global curvilinear co-ordinates irregular non-orthogonal unstructured grids analysis of printed circuit devices using the planar generalized Yee algorithm. Part 12 The body of revolution FD-TD algorithm, Thomas Jurgens and Gregory Saewert: field expansion difference equations for on-axis cells numerical stability PML absorbing boundary condition. Part 13 Modelling of electromagnetic fields in high-speed electronic circuits, Piket-May and Taflove. (part contents).
Citations
More filters
DOI•
TL;DR: In this paper , a dispersive finite-difference time-domain (FDTD) method based on the recursive integration (RI) technique for the modeling of the lossy multipole Debye dispersive media is described.
Abstract: A dispersive finite-difference time-domain (FDTD) method based on the recursive integration (RI) technique for the modeling of the lossy multipole Debye dispersive media is described in this article. The interaction between the electromagnetic (EM) field and the human tissues is simulated by means of the RI method, and the frequency-dependent formulations which possess good compatibility with the main FDTD algorithm are achieved. Next, the expression of the multipole Debye dispersion model is similar to the multipole complex frequency shift (CFS) stretching function which is utilized to build the multipole perfectly matched layer (MPML). Therefore, a significant feature of using the RI method is its overall modeling of both multipole Debye dispersive media and MPML boundary conditions. Furthermore, the stability analysis of the RI method in solving the lossy multipole Debye dispersive model indicates that the Courant–Friedrich–Levy (CFL) stability limit of the regular FDTD can be maintained. At last, the numerical cases performed in this work demonstrate the correctness of the RI method in modeling dispersive media.
DOI•
14 Nov 2022
TL;DR: In this paper , the effects of the loop design, load resistance, and positions of load connection on the sensitivity of a ferrite antenna for receiving UWB (ultra-wideband) electromagnetic pulses of the nanosecond duration range has been studied.
Abstract: Ferrite antenna for receiving UWB (ultra-wide-band) electromagnetic pulses of the nanosecond duration range has been considered. The influences of the loop design, load resistance, and positions of load connection on the sensitivity of the antenna have been studied. The method of finite differences in the time domain has been used for numerical simulation. During the investigation, the loop was transformed into a cylinder with a slot covering a ferrite rod. Analysis was done for such antenna design parameters as the geometry of the loop, load resistance, and position of loads in the slot of the loop. The dispersion properties of ferrite in the form of the Debye condition of the 1st order are taken into account. It obtained regularities leading to an increase in the ferrite antenna sensitivity.
TL;DR: In this article , a one-step Crank-Nicolson Direct-Splitting (CNDS) algorithm is proposed to evaluate the electrical behavior of satellite sensors under the low-pressure discharge circumstance.
Abstract: Low-pressure discharge causes air ionization resulting in performance degeneration or failure for the satellite sensors in outer space. Here, a one-step Crank-Nicolson Direct-Splitting (CNDS) algorithm is proposed to evaluate the electrical behavior of satellite sensors under the low-pressure discharge circumstance. To be more specific, the CNDS algorithm is proposed in the Lorentz medium, which can accurately analyze the ionized air and generated plasma. Higher order perfectly matched layer (PML) is modified in the Lorentz medium to efficiently terminate the unbounded lattice. It can be concluded that the proposed algorithm shows entire considerable performance in the low-pressure discharge evaluation. The proposed PML formulation behaviors enhanced absorbing performance compared with the existing algorithm. Through the experiments, it can be observed that the low-pressure discharge phenomenon causes performance variation, which shows a significant influence on the satellite sensors. Meanwhile, results show considerable agreement between the simulation and experiment results which indicates the effectiveness of the algorithm.
TL;DR: In this paper , a finite element scheme for solving the time-dependent Maxwell's equations on unstructured grids is studied, which has one degree of freedom for most edges and a sparse inverse mass matrix.
Abstract: A novel finite element scheme is studied for solving the time-dependent Maxwell's equations on unstructured grids efficiently. Similar to the traditional Yee scheme, the method has one degree of freedom for most edges and a sparse inverse mass matrix. This allows for an efficient realization by explicit time-stepping without solving linear systems. The method is constructed by algebraic reduction of another underlying finite element scheme which involves two degrees of freedom for every edge. Mass-lumping and additional modifications are used in the construction of this method to allow for the mentioned algebraic reduction in the presence of source terms and lossy media later on. A full error analysis of the underlying method is developed which by construction also carries over to the reduced scheme and allows to prove convergence rates for the latter. The efficiency and accuracy of both methods are illustrated by numerical tests. The proposed schemes and their analysis can be extended to structured grids and in special cases the reduced method turns out to be algebraically equivalent to the Yee scheme. The analysis of this paper highlights possible difficulties in extensions of the Yee scheme to non-orthogonal or unstructured grids, discontinuous material parameters, and non-smooth source terms, and also offers potential remedies.
TL;DR: The discrete exterior calculus (DEC) is a generalization of the finite difference time domain (FDTD) method for photonic crystal (PC) waveguides as discussed by the authors , which enables efficient time evolution by construction and fits well for nonhomogeneous computational domains and obstacles of curved surfaces.
Abstract: The discrete exterior calculus (DEC) is very promising, though not yet widely used, discretization method for photonic crystal (PC) waveguides. It can be seen as a generalization of the finite difference time domain (FDTD) method. The DEC enables efficient time evolution by construction and fits well for nonhomogeneous computational domains and obstacles of curved surfaces. These properties are typically present in applications of PC waveguides that are constructed as periodic structures of inhomogeneities in a computational domain. We present a two‐dimensional DEC discretization for PC waveguides and demonstrate it with a selection of numerical experiments typical in the application area. We also make a numerical comparison of the method with the FDTD method that is a mainstream method for simulating PC structures. Numerical results demonstrate the advantages of the DEC method.