Late-time Instability Research Articles

A COMPARISON OF MARCHING-ON IN TIME METHOD WITH MARCHING-ON IN DEGREE METHOD FOR THE TDIE SOLVER

One of the most popular methods to solve a time domain electric field integral equation (TD-EFIE) is the marching-on-in-time(MOT) method. Recently, a new method called marching-on-in- degree(MOD) that uses Laguerre polynomials as temporal basis functions has been developed to eliminate the late time instability of the MOT method. A comparison is presented between these two methods from the standpoint of formulation, stability, cost and accuracy. Numerical results are presented to illustrate these features in the comparison.

A Comparison of Performance of Four Methods in Solving Time Domain Integral Equations for Arbitrarily Shaped Conducting Bodies

The objective of this paper is to generate a temporal response of three dimensional conducting structures by solving time domain electric-field integral equation. Four methods including Initial MOT/ averaging MOT/ IMPT/ MOO are used to solve the integral equation. Comparison of performance of four methods is presented to illustrate validity for solving late-time instability by simulation of four targets including two simple and two complex conducting bodies. DOI: 10.2529/PIERS060906091850

Analysis of Millimeter Wave Microstrip Circulator with a Magnetized Ferrite Sphere by FDTD Method with Modified Matrix Pencil Method

In this paper, the modified matrix pencil (MMP) method is used in the finite difference time domain (FDTD) method to eliminate the late time instability of time domain responses when analyzing the novel microstrip circulator with a magnetized ferrite sphere. The frequency dependent scattering parameters: reflection, isolation and insertion parameters of the microstrip circulator calculated over a wide band of frequencies with this hybrid method are compared with that obtained by direct FDTD method which agree well with the experimental results.

Anisotropic-Medium PML for Vector FETD With Modified Basis Functions

A novel anisotropic-medium perfectly matched layer (PML) implementation is presented for boundary truncation in the three-dimensional vector finite-element time-domain (FETD) method. This approach utilizes a complex set of vector test and basis functions in the PML region, that recover the usual basis functions in the non-PML region. Numerical examples show that the proposed PML-FETD approach has small reflection errors and no observed late-time instabilities for simulations involving up to 10/sup 6/ time steps.

A new stable hybrid three-dimensional generalized finite difference time domain algorithm for analyzing complex structures

In this paper, we propose a new stable hybrid, three-dimensional (3-D), generalized finite difference time domain algorithm-formulated by using of the cell method (CM) (a finite volumes type method)-designed to analyze objects with fine details without using very small time steps dictated by the Courant condition. The new algorithm is an extension to the 3-D cases of an analogous hybrid two-dimensional algorithm, also formulated by the CM, and presented earlier by the authors in a previous publication. We carry out a detailed analysis of the stability of the proposed algorithm, paying special attention to the phenomenon of late time instabilities. Finally, the results of some numerical tests are provided to show the absence of instabilities and the efficiency of the hybrid algorithm.

A stable solution of time domain electric field Integral equation for thin-wire antennas using the Laguerre polynomials

In this paper, a numerical method to obtain an unconditionally stable solution of the time domain electric field integral equation for arbitrary conducting thin wires is presented. The time-domain electric field integral equation (TD-EFIE) technique has been employed to analyze electromagnetic scattering and radiation problems from thin wire structures. However, the most popular method to solve the TD-EFIE is typically the marching-on in time (MOT) method, which sometimes may suffer from its late-time instability. Instead, we solve the time-domain integral equation by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically and stable results can be obtained even for late-time. Furthermore, the excitation source in most scattering and radiation analysis of electromagnetic systems is typically done using a Gaussian shaped pulse. In this paper, both a Gaussian pulse and other waveshapes like a rectangular pulse or a ramp like function have been used as excitations for the scattering and radiation of thin-wire antennas with and without junctions. The time-domain results are compared with the inverse discrete Fourier transform (IDFT) of a frequency domain analysis.

A Theoretical Study of the Stability Criteria for Hybridized FDTD Algorithms for Multiscale Analysis

In this paper, we propose two new hybrid, two-dimensional, generalized finite-difference time-domain algorithms-formulated by using the cell method-and designed to analyze objects with fine details, without using very small time steps dictated by the Courant condition. A detailed analysis of the stability of the proposed algorithms is presented, with special attention devoted to the phenomenon of late time instabilities. Finally, some rules are provided that would ensure the stability of the proposed algorithms.

Stable non-orthogonal FDTD method

Introduction: A number of techniques have been proposed to extend the classical Yee’s finite-difference time-domain (FDTD) algorithm to a grid that is conformal to curved objects. Such methods, including the nonorthogonal FDTD (NFDTD) [1, 2], can accurately represent the curved boundaries without resorting to inefficient staircase orthogonal meshes. However, their significant advantage is offset by the fact that they suffer from late time instabilities. In [3], it is demonstrated that the instability of NFDTD is inherent. Although a ‘time-subgriding’ approach is presented there to reduce the late time instability, an unconditionally stable NFDTD is still not obtained. In this Letter, we introduce a novel approach to discretise Maxwell’s equations using only the covariant components. It is demonstrated that the new NFDTD algorithm is stable over a very long period of numerical simulation. Moreover, the algorithm is less computationally intensive than other NFDTD methods [1, 2] where both of the covariant and contravariant components are needed. The proposed technique is validated by simulation results on a circular waveguide resonator.

A comparison of time‐domain hybrid solvers for complex scattering problems

AbstractIn this paper the accuracy, efficiency and stability of two hybrid solvers are compared to FDTD in several complex scattering cases. The explicit hybrid solver, FD‐FV, combines an unstructured FVTD solver with FDTD, and the explicit–implicit solver, FD‐FE, combines an unstructured FETD solver with FDTD.The results show that the two hybrid solvers are much more efficient than FDTD for complex objects where a Cartesian grid is not able to capture the geometry properly. Furthermore, they show that the FD‐FE solver is a better choice than the FD‐FV solver. Mainly because it is stable as long as the time step satisfies the CFL condition in the FDTD region, while the FD‐FV solver may suffer from late time instabilities. But the FD‐FE solver is also more efficient since the iterative method used to solve the matrix–vector system arising in FETD converges fast and the FVTD solver is heavily penalized by having to take shorter time steps to satisfy its CFL condition. Copyright © 2002 John Wiley & Sons, Ltd.

Reduction of late time instabilities of the finite-difference time-domain method in curvilinear co-ordinates

Reduction of late time instabilities of the finite-difference time-domain method in curvilinear co-ordinates

Suppression of late-time instabilities in 3-D-FDTD analyses by combining digital filtering techniques and efficient boundary conditions

A new computational procedure is developed to suppress late-time instabilities in three-dimensional finite-difference time-domain analyses. The method combines low-pass filtering schemes with absorbing boundary conditions. The computational domain is truncated at only a few cells from the scattering object. Applications concern the analysis of long transients exciting frequencies up to a few megahertz.

Numerical stability of nonorthogonal FDTD methods

In this paper, a sufficient test for the numerical stability of generalized grid finite-difference time-domain (FDTD) schemes is presented. It is shown that the projection operators of such schemes must be symmetric positive definite. Without this property, such schemes can exhibit late-time instabilities. The origin and the characteristics of these late-time instabilities are also uncovered. Based on this study, nonorthogonal grid FDTD schemes (NFDTD) and the generalized Yee (GY) methods are proposed that are numerically stable in the late time for quadrilateral prism elements, allowing these methods to be extended to problems requiring very long-time simulations. The study of numerical stability that is presented is very general and can be applied to most solutions of Maxwell's equations based on explicit time-domain schemes.

Analysis of transient scattering from composite arbitrarily shaped complex structures

A time-domain surface integral equation approach based on the electric field formulation is utilized to calculate the transient scattering from both conducting and dielectric bodies consisting of arbitrarily shaped complex structures. The solution method is based on the method of moments (MoM) and involves the modeling of an arbitrarily shaped structure in conjunction with the triangular patch basis functions. An implicit method is described to solve the coupled integral equations derived utilizing the equivalence principle directly in the time domain. The usual late-time instabilities associated with the time-domain integral equations are avoided by using an implicit scheme. Detailed mathematical steps are included along with representative numerical results.

Practical aspects of higher-order numerical schemes for wave propagation phenomena

This paper examines practical issues related to the use of compact-difference-based fourth- and sixth-order schemes for wave propagation phenomena with focus on Maxwell's equations of electromagnetics. An outline of the formulation and scheme optimization is followed by an assessment of the error accruing from application on stretched meshes with two approaches: transformed plane method and physical space differencing. In the first technique, the truncation error expansion for the sixth-order compact scheme confirms that the order of accuracy is preserved if a consistent mesh refinement strategy is followed and further that metrics should be evaluated numerically even if analytic expressions are available. Physical space-differencing formulas are derived for the five-point stencil by expressing the coefficients in terms of local spacing ratios. The order of accuracy of the reconstruction operator is then verified with a numerical experiment on stretched meshes. To ensure stability for a broad range of problems, Fourier analysis is employed to develop a single-parameter family of up to tenth-order tridiagonal-based spatial filters. The implementation of these filters is discussed in terms of their effect on the interior scheme as well as in a 1-D cavity where they are employed to suppress a late-time instability. The paper concludes after demonstrating the application of the scheme to several 3-D canonical problems utilizing Cartesian as well as curvilinear meshes. Published in 1999 by John Wiley & Sons, Ltd. This article is a U.S. Government work and is in the public domain in the United States.

Treating late-time instability of hybrid finite-element/finite-difference time-domain method

The hybrid finite element/finite-difference time-domain (FETD/FDTD) method previously proposed to handle arbitrarily shaped dielectric objects is employed to investigate electromagnetic problems of high Q systems for which the transient response over a very long duration is necessary. To begin with, the paper demonstrates that this hybrid method may suffer from late-time instability and spurious DC modes. Then an approach which combines the temporal filtering and frequency shifting techniques is presented to overcome sequentially and, respectively, the two drawbacks. Its accuracy is validated by the favorable comparison with several different methods for the analysis of resonant frequencies and and factors of the various modes in an isolated dielectric resonator. Finally, the present method is applied to calculate the scattering parameters on the microstrip line due to the presence of the cylindrical dielectric resonator.

An investigation into the properties of the FDTD mesh with application to wires and strips

The analysis of structures which contain thin wires or narrow microstrips using the FDTD method and without resorting to a very fine mesh, has been an area of intensive research for many years. Despite this activity, however, the problem is still not definitively solved. In this paper the problem is attacked by investigating the properties of the FDTD mesh when the material parameters of a single cell, or a small group of cells, are altered. From this, formulae are derived by which these parameters may be chosen in order to accurately represent a conductor of small cross-section. Results are presented which show that accurate results for wire and microstrip transmission lines can be achieved with little or no computational overhead and without the problems of late time instability or spurious field divergence. Copyright © 1999 John Wiley & Sons, Ltd.

Passive equivalent circuit of FDTD: An applicationto subgridding

The finite difference time domain (FDTD) method gives accurate results for many problems but uses a large amount of computer memory and time. This can be reduced by using subgrids (fine grids) only around critical areas in the problem domain. The fields within the coarse and fine grids are found using standard FDTD equations, while at the boundary of the subgrid, interpolation of coarse grid fields is utilised. However, a simple interpolation as reported in literature exhibits late time instability. The authors present a stable scheme of updating the subgrid boundary fields by replacing the grid discontinuity with an equivalent circuit. The stability and accuracy of this new scheme is demonstrated through calculation of the cutoff wavelength of a dielectric slab loaded waveguide for various slab thickness.

Transient scattering from three-dimensional arbitrarily shaped dielectric bodies

A surface integral equation approach is utilized to calculate the transient scattering from arbitrarily shaped, three-dimensional dielectric bodies illuminated by an incident electromagnetic pulse. The surface of the dielectric body is discretized with triangular patches so that fairly arbitrarily shaped objects may be modeled. The Poggio–Miller–Chang–Harrington–Wu [ R. Mittra , Computer Techniques for Electromagnetics ( Pergamon, Oxford, 1973)] formulation, in conjunction with the marching-on-in-time method, is used to derive explicit expressions for the present-time currents as a function of the incident field and the past history. The late-time instabilities are suppressed by use of a simple averaging scheme. Finally, sample results showing various geometries are presented and are compared with other numerical techniques.

Optimized absorbing boundary conditions for the analysis of planar circuits using the finite difference time domain method

It is shown that the description of absorbing boundary condition algorithms (ABCs) in terms of single incident plane waves does not provide sufficient information for choosing the best ABC for planar waveguide termination. A technique for optimizing the ABCs that results in a return loss from a wideband pulse less than -50 dB is demonstrated. This technique reduces the risk of loss of accuracy due to mode conversion at the boundary. The use of these optimized ABCs considerably improves analysis results for an important category of microstrip components. For boundaries transverse to the direction of propagation, it is shown that inaccuracy and late time instability can result if the boundary is placed in regions of high field strength.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Treatment of Late Time Instabilities in Finite-Difference EMP Scattering Codes

Time-domain solutions to the finite-differenced Maxwell's equations give rise to several well-known nonphysical propagation anomalies. In particular, when a radiative electric-field look back scheme is employed to terminate the calculation, a high-frequency, growing, numerical instability is introduced. This paper describes the constraints made on the mesh to minimize this instability, and a technique of applying an absorbing sheet to damp out this instability without altering the early time solution. Also described are techniques to extend the data record in the presence of high-frequency noise through application of a low-pass digital filter and the fitting of a damped sinusoid to the late-time tail of the data record. An application of these techniques is illustrated with numerical models of the FB-111 aircraft and the B-52 aircraft in the in-flight refueling configuration using the THREDE finite difference computer code. Comparisons are made with experimental scale model measurements with agreement typically on the order of 3 to 6 dB near the fundamental resonances.