A Hybrid Numerical Method for Loaded Highly Resonant Single Mode Cavities

Hile, Cheryl V.; Kriegsmann, Gregory A.

doi:10.1006/jcph.1998.5951

Cited by 9 publications

(5 citation statements)

References 13 publications

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“…This is not necessary, but simplifies the computation. Although these models are highly idealized, the general solution method might have direct application in the technology of sintering ceramic materials by means of microwave energy, see for example Hile & Kriegsmann (1998).…”

Section: Resonances In Two-dimensional Laterally Periodic Open Systemsmentioning

confidence: 99%

On resonances in open systems

Hein¹,

Hohage

Koch³

2004

J. Fluid Mech.

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An open system or open resonator is a domain of wave activity separated from the exterior by a partly open or partly transparent surface. Such open resonators lose energy to infinity through radiation. The numerical computation of the corresponding resonances is complicated by spurious reflections of the outgoing waves at the necessarily finite grid boundaries. These reflections can be reduced to extremely low levels by applying perfectly matched layer (PML) absorbing boundary conditions, which separate the discrete resonances from the continuous spectrum. Using a simple one-dimensional model problem, the influence of the various PML parameters is determined by a numerical error analysis. In addition to one-dimensional open resonators, two-dimensional open resonators as well as various resonating structures in waveguides are considered, and the resonant spectra and selected modes are evaluated. For the first time, leaky modes are computed for several resonating structures in a waveguide in addition to the trapped modes published in the literature. In applications, leaky mode resonances are often more important than trapped mode resonances. Gap tones, observed in a model problem of high-lift configurations, are identified as transversal resonant modes with the lowest radiation losses.

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Section: Resonances In Two-dimensional Laterally Periodic Open Systemsmentioning

confidence: 99%

On resonances in open systems

Hein¹,

Hohage

Koch³

2004

J. Fluid Mech.

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“…Corresponding to the n $ unit modal excitation and with the edge-element/Galerkin choice W"N H in Equation (30), this FEM procedure gives Once this solution has been achieved it is possible to recreate the scattering matrix of the object-in-waveguide in exactly the same way as indicated for the simpler situations described. It may be noted that at the frequencies of interest in most practical cases * itself will be non-resonant, thus the problem of ill-conditioned "nite element matrices [5] should not arise while, in any case, the volume of the FEM discretization is reduced to an absolute minimum.…”

Section: Applications Of the Discretised Huygens Equationmentioning

confidence: 99%

“…However, there are situations in which parallel planes conform poorly with the scattering object, de"ning a largely empty region, so that the numerical procedure becomes ine$cient. Indeed when the "nal objective is to model, by FEM, a multimode cavity such as a short-circuit loaded waveguide, the planar-boundary FEM region may itself represent a high-Q cavity, its matrices becoming ill-conditioned even though the object itself is non-resonant [5].…”

Section: Introductionmentioning

confidence: 99%

An extended Huygens' principle for modelling scattering from general discontinuities within hollow waveguides

Ferrari

2001

Int J Numerical Modelling

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SUMMARYThe modal "elds, generalized scattering matrix (GSM) theory and dyadic Green's functions relating to a general uniform hollow waveguide are brie#y reviewed in a mutually consistent normalization. By means of an analysis linking these three concepts, an extended version of the mathematical expression of Huygens' principle is derived, applying to scattering from an arbitrary object within a hollow waveguide. The integral-equation result expresses the total "eld in terms of the incident waveguide modal "elds, the dyadic Green's functions and the tangential electromagnetic "eld on the surface of the object. It is shown how the extended principle may be applied in turn to perfect conductor, uniform material and inhomogeneous material objects using a quasi method of moments (MM) approach, coupled in the last case with the "nite element method. The work reported, which indicates how the GSM of the object may be recovered, is entirely theoretical but displays a close similarity with established MM procedures.

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“…For instance, the convergence of the field in the vicinity of the iris demands a very fine spatial discretisation because of the modal composition of the field in that region. Another problem that arises with frequency‐domain FEM is that it leads to an ill‐conditioning matrix because of the resonant character of the applicator [2]. If one takes into account that the electromagnetic problem is solved many times, because of the thermal–electromagnetic coupling, those problems become even more critical.…”

Section: Introductionmentioning

confidence: 99%

Decision criterion based on sensitivity analysis to solve microwave heating in a single‐mode cavity

Oliveira

Silva

Batalha

2014

IET Science, Measurement & Technology

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This study presents advances in microwave heating simulations in a single-mode rectangular cavity via numerical method. The main contribution of this work is to propose a new decision criterion that provides the instant when the electric field must be recalculated when solving the thermal-electromagnetic problem inside the cavity. In most cases, the decision criteria found in the literature are empirically based on the variation of the loss factor. In this work, it is shown that the authors may introduce significant errors in the results and/or increase the simulation time. Here, the decision criterion is based on sensitivity analysis techniques that evaluate the derivative of the electric field with respect to the complex permittivity. Numerical results show that the new decision criterion works well for different load conditions and can be easily implemented with a hybrid analytical-finite element method.

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A Hybrid Numerical Method for Loaded Highly Resonant Single Mode Cavities

Cited by 9 publications

References 13 publications

On resonances in open systems

On resonances in open systems

An extended Huygens' principle for modelling scattering from general discontinuities within hollow waveguides

Decision criterion based on sensitivity analysis to solve microwave heating in a single‐mode cavity

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