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The Averaging Effect on Resonant Frequency Calculations of a Partially Filled Microwave Cavity Using FDTD Method
... For the proper treatment of the dielectric interface in the FDTD solution, principally, the two main techniques are (i) averaging techniques (arithmetic, harmonic, and geometric averaging) based on an effective dielectric permittivity [2][3][4] and (ii) a dielectric functioning (DF) technique with different distances [11,12]. The effect of the DF technique on the accuracy of the PDFC resonance frequencies has not been investigated yet and is completely unknown, although the accuracy effect of the averaging techniques on the PDFC resonance frequencies are performed in previous studies [5,6]. The effects of the different spatial resolutions are also critical for the FDTD numerical dispersion error. ...
... However, the application of the numerical methods without any treatment of the dielectric interface may lead to unignorable errors [5,6]. Specifically, for the rectangular PDFC problems, two examples can be given. ...
... Principally, not only arithmetic averaging but also harmonic averaging, geometric averaging, and some of their derivatives can be used for the proper interface modeling [10]. In this sense, second, it is proved for the PDFC problem in our previous publications that the accuracy effect of the arithmetic, the harmonic, and the geometric averaging on the treatment of the dielectric interface is severe [5,6]. Moreover, different averaging techniques are performed well for low-and high-contrast material fillings. ...
In this study, accuracy analyses of resonance frequency calculations for a three‐dimensional partially dielectric‐filled cavity are investigated by using finite difference time domain (FDTD) method. The calculations are performed for low‐ and high‐contrast lossless dielectric materials. In order to excite multicavity modes, the cavity is driven by a Gaussian pulse source. The main error sources for the numerical resonance frequency calculations of the partially dielectric‐filled cavity are (i) applied technique for treatment of a dielectric interface between free space and material medium and (ii) numerical dispersion of the FDTD method. The effects of these errors are analyzed both in detail. A no averaging (without any averaging), a proper averaging technique for the low‐/high‐contrast case, and the dielectric functioning technique with three different distances of 3∆z,5∆z,and7∆z are applied for the treatment of dielectric interface. Additionally, four spatial resolutions of λ⁄10, λ⁄20, λ⁄30, and λ⁄40 are used for the numerical dispersion analyses. The calculated results are compared with a semianalytical solution for the accuracy evaluations. Specially, in order to explain ordering of numerical errors for each case, a technique based on electromotor force emf calculation is proposed with good success. The computational advantages of the applied techniques are also shown over no averaging case.
... A semi-analytical solution of the partially dielectric filled cavity (PDFC) is found by extracting transcendental equation of two different mediums in which a transverse resonance method is used for a partially filled rectangular waveguide [Balanis, 1989]. As an example, the dispersion equation for the Transverse Magnetic (TM ) modes where , , are the mode numbers is given by [Ertay et al., 2017], [Li et al., 2020], [Bişkin et al., 2021] − tan( [ℎ − ]) = tan( ) = √ 2 − 2 − 2 ; = √ 2 − 2 − 2 (6.14) ...
In this thesis, numerical analysis of Nonuniform Finite Difference Time Domain (NU FDTD) method is investigated in detail. A nonuniform numerical dispersion equation (NU NDE) is formulated after extraction of the NU FDTD update equations in three-dimensional Cartesian coordinates.
Two numerical examples of an empty cavity and a partially loaded cavity are considered for the accuracy analyses of a uniform mesh, a NU Chebyshev-Gauss-Lobatto (NU CGL) mesh (This mesh is used, for the first time, in the NU FDTD solution) and a NU Linear mesh. Specially, a single- and multi-mode cavity excitations are considered by using monochromatic and wideband pulse sources for two different Courant-Friedrichs-Lewy (CFL) numbers.
In the numerical accuracy evaluations, signals in time domain, resonance peaks in frequency domain and field distributions in space domain are used for comparisons with an analytical solution. Specially, a semi-analytical solution is used for the partially loaded cavity.
The numerical results for the empty cavity show that the uniform mesh gives the most accurate results. The NU CGL mesh comes second and the NU Linear mesh gives the worst results. However, the numerical results for the partially loaded cavity show that the NU CGL mesh gives the most accurate results. The uniform mesh comes second and the NU Linear mesh dives the worst results. All these numerical results also correspond to the results of the numerical dispersion equation.
The main conclusion of this thesis is that additional researches are necessary for better understanding of the NU FDTD numerical solution of the partially loaded cavity problem for different meshes since the effect of the material inhomogeneity (different permittivities) on the solution accuracy has not been known yet.
In this study, resonance frequencies of a cubic resonator filled with a partial dielectric material are calculated using Finite Difference Time Domain (FDTD) method. The resonator's field distributions and time domain behaviors are investigated using a point Gaussian pulse type hard source. The resonance frequencies obtained by transforming the calculated time domain signals to the frequency domain with Fast Fourier Transform (FFT) are compared with the analytical results. The resonance frequency calculation errors are reduced by applying an averaging technique and a high-resolution gridding for the field discontinuity observed at a dielectric interface.
In computational electromagnetics, the advantages of the standard Yee algorithm are its simplicity and its low computational costs. However, because of the accuracy losses resulting from the staircased representation of curved interfaces, it is normally not the method of choice for modelling electromagnetic interactions with objects of arbitrary shape. For these problems, an unstructured mesh finite volume time domain method is often employed, although the scheme does not satisfy the divergence free condition at the discrete level. In this paper, we generalize the standard Yee algorithm for use on unstructured meshes and solve the problem concerning the loss of accuracy linked to staircasing, while preserving the divergence free nature of the algorithm. The scheme is implemented on high quality primal Delaunay and dual Voronoi meshes. The performance of the approach was validated in previous work by simulating the scattering of electromagnetic waves by spherical 3D PEC objects in free space. In this paper we demonstrate the performance of this scheme for penetration problems in lossy dielectrics using a new averaging technique for Delaunay and Voronoi edges at the interface. A detailed explanation of the implementation of the method, and a demonstration of the quality of the results obtained for transmittance and scattering simulations by 3D objects of arbitrary shapes, are presented.
Accuracy degradation at a dielectric interface in simulations using the finite-difference time-domain method can be prevented by assigning suitable effective permittivities at the nodes in the vicinity of the interface. The effective permittivities with exact second-order accuracy at the interface inclined to the Yee-lattice axis are analytically derived for what we believe to be the first time. We discuss two interfaces with different inclined angles between their normal and the Yee-lattice axis in the case of two-dimensional TE polarization. The tangent of the angle is 1 for one interface and 1 / 2 for the other. With the derived effective permittivities, reflection and transmission at the interface are simulated with second-order accuracy with respect to cell size. The accuracy is demonstrated by numerical examples.
In this paper, a comparison study of dielectric loaded effects of rectangular resonant cavity in terms of resonance frequency, dielectric loading rate and various dielectric constant for different 𝑻𝑬𝒚 and 𝑻𝑴𝒚 modes is presented. This study includes two stage analysis procedures. Firstly, field expressions and
resonance frequency of the dielectric loaded rectangular resonant cavity with respect to dielectric loading rate are obtained for different 𝑻𝑬𝒚 and 𝑻𝑴𝒚 modes by using semi-analytical approach.
Secondly, perturbation method is applied for acquiring resonance frequency of each chosen different mode and dielectric constant with respect to dielectric loading rate. Comparison of two different
method in terms of variation of resonant frequency with respect to relative dielectric thickness is performed for different dielectric loading case for the same mode and different modes for the same
dielectric loading. The results show that perturbation approach can be good alternative to semi-analytical method to calculate the variation of the resonant frequency with respect to relative
dielectric thickness.
In this paper, an investigation of the microwave heating of a lossy material located inside a cavity by the Finite-Difference Time-Domain (FD-TD) method is undertaken. The emphasis of this workfocuses on the performance of the FD-TD method when certain traditional assumptions are used within the framework of the model. The limitations of these assumptions will be deliberated and more accurate counterparts will be proposed and tested. In particular, it will be shown that when only a single mode is assumed to exist around the aperture between the waveguide and the cavity, spurious numerical results arise. Further, the numerical simulation indicates that the treatment of the interfacial boundary condition located between free-space and the material becomes very important when predicting the dissipated power distribution for a lossy dielectric material. A new approximation of this interfacial boundary condition is developed and a comparison between existing and new methodologies is made. The treatment of singular field behavior near sharp edges of the cavity is also examined and a study of the effect of using different techniques to model regions where this condition arises is presented. In order to validate the numerical simulation results, comparisons against experimental data sets previously reported in the literature will be made. In summary, the new techniques proposed in this research yield a solution of high accuracy and demonstrate an increased flexibility for simulating microwave systems. It will be shown that the FD-TD method satisfies the important Maxwell equation field divergence condition everywhere within the applicator.
A cavity with a time signal applied taken jointly is treated as a time variant physical system. Standard formulation of the boundary-value problem for system of Maxwell's equations (with ∂t) is supplemented with the initial conditions and the causality principle. It is proved that electromagnetic field can be presented as the classical decompositions in terms of the solenoidal and irrotational modes but with time dependent modal amplitudes. For the latters, evolutionary (i.e., with time derivative) ordinary differential equations are derived and solved analytically, in quadratures. Simple explicit solutions (in elementary functions) for the modal amplitudes as functions of time are obtained in a particular case. Numerical examples are exhibited, time-domain resonances are studied.
In Yee's finite-difference time-domain (FDTD) scheme, effective permittivities are often used to account for offsets of dielectric interfaces from grid nodes. The specific values of these effective permittivities must be chosen in such a way that the second-order accuracy of the scheme is preserved. It is shown in this work that, contrary to more elaborate techniques proposed recently for the development of these effective permittivities, a rigorous application of the integral forms of Maxwell's curl equations on the Yee's lattice leads to the desired values in a straightforward fashion. Numerical experiments in a two-dimensional (2-D) cavity are used to verify that the calculated effective permittivities preserve the second-order accuracy of the FDTD scheme.
In this paper, the finite-difference time-domain (FDTD) method is
applied to calculate the resonant frequency of dielectric resonators
(DRs) with curved surface. The contour-path integral FDTD (CFDTD) is
modified to deal with the curved surface of the dielectric body while
the traditional rectangular cells are maintained. Results are compared
with theoretical values and staircase approximation, and show that the
present method is more accurate than the staircase approximation
Zaman Uzayi Sonlu Farklar (FDTD) Yöntemi, Web Book
- S Aksoy
S. Aksoy, Zaman Uzayı Sonlu Farklar (FDTD) Yöntemi, Web Book,
Gebze Technical University, Kocaeli, Turkey, 2021, (in Turkish).
The investigation of source location effect for resonant modes of a cubic cavity
- E Basaran
- S Aksoy
- A A Ergin
E. Başaran, S. Aksoy and A. A. Ergin, "The investigation of source
location effect for resonant modes of a cubic cavity," 3. International
Conference on Mathematical & Computational Applications, pp. 41-47,
Selcuk Unversity, Konya, Turkey, 2002.
The investigation of source location effect for resonant modes of a cubic cavity
- basaran