A difference scheme for the non-stationary maxwell equations in waveguide systems

Maikov, A. R.; Sveshnikov, A. G.; Yakunin, S. A.

doi:10.1016/0041-5553(86)90126-6

Cited by 4 publications

(12 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The solutions that satisfy the zero initial conditions and are free from any components propagating along the decreasing z j . This formula is derived through the integral Laplace transform over t or the Fourier cosine transform over z j [ Maikov et al , 1986]. Actually, on the assumption that at the initial moment of time t = 0 the excitation wave U j ( g , t ) has not yet reached the discontinuity boundary in the plane z 1 = 0, we obtain for the amplitudes { w nj ( z j , t )} a sequence of homogeneous initial boundary value problems: By using in the Fourier cosine transform over z j at the semi‐axes z j ≥ 0 (image ↔ original) we obtain the following Caushy problems for the images nj (ω, t ): Here we had taken into account that the waves U j s ( z j , t ) are free of components propagating along the decreasing z j .…”

Section: Evolutionary Basis Of the Signal And Transform Operatorsmentioning

confidence: 99%

Section: Essential Definitionsmentioning

confidence: 99%

See 1 more Smart Citation

Time domain theory of open waveguide resonators: Canonical problems and a generalized matrix technique

Sirenko

Yashina

2003

Radio Science

View full text Add to dashboard Cite

[1] In this paper, we consider new solutions and algorithms for initial boundary-value problems in the electromagnetic theory of open waveguide resonators. The approaches are based on a description of the scattering properties of such resonators in terms of the transform operators for an evolutionary basis of the non-stationary signal, that have the same significance in the course of analyses in time domain as generalized scattering matrixes in frequency domain. All suggested approaches imply using mathematically correct computational procedures at the key stages of forming the solution, in particular, the analytical regularization method-the semi-inversion method.

show abstract

Section: Evolutionary Basis Of the Signal And Transform Operatorsmentioning

confidence: 99%

Section: Essential Definitionsmentioning

confidence: 99%

Time domain theory of open waveguide resonators: Canonical problems and a generalized matrix technique

Sirenko

Yashina

2003

Radio Science

View full text Add to dashboard Cite

show abstract

“…Exact absorbing conditions (EAC) are used in computational electrodynamics of nonsine waves for truncating the domain of computation when replacing the original open initial boundary value problem by a modified problem formulated in a bounded domain [1][2][3][4][5][6][7][8][9]. In the present work, we construct and analyze the EAC as applied to the axially symmetrical waveguide structures illuminated by symmetrical pulsed TEand TM-waves (or TE 0 -and TM 0 -waves) and prove the equivalency of the original (open) and modified (closed) initial boundary value problems.…”

Section: Introductionmentioning

confidence: 99%

The Exact Absorbing Conditions Method in the Analysis of Open Electrodynamic Structures: Circular and Coaxial Waveguides

Sautbekov¹,

Sirenko²,

Velychko³

et al. 2014

International Journal of Antennas and Propagation

View full text Add to dashboard Cite

show abstract

“…They have already taken their proper place in electromagnetic simulation in fundamental and applied electromagnetics. In 1986, scientists from Moscow State University, Ⱥ. R. Maikov, A. G. Sveshnikov, and S. A. Yakunin, published their paper [18]. In this paper the exact non-local conditions for virtual boundaries in regular semi-infinite hollow waveguides (with constant cross section), serving as channels for signals propagating from certain resonant junctions, were formulated for the fist time.…”

mentioning

confidence: 97%

“…In this paper the exact non-local conditions for virtual boundaries in regular semi-infinite hollow waveguides (with constant cross section), serving as channels for signals propagating from certain resonant junctions, were formulated for the fist time. Later on (see for example, references [19]-[29]) the approach suggested in [18], that is based on the utilization of radiation conditions for time-spatial amplitudes of outgoing modes, has been modified for various electromagnetic problems: antenna design, analysis and synthesis problems for quasi optical open resonators with dispersive elements, electromagnetic monitoring of human environment and others. For several particular cases the problems of non-locality, the problems of large and distant sources and the problem of corner points, points of intersection of coordinate boundaries, have been resolved in a rigorous way.…”

mentioning

confidence: 99%

`Fully Absorbing' Boundary Conditions in the `Open' Electrodynamic Problems for Pulsed Waves

Sirenko¹

2006 International Conference on Mathematical Methods in Electromagnetic Theory

View full text Add to dashboard Cite

The paper presents novel results associated with the algorithmization and solution of model initial boundary-value problems describing transformations of pulsed electromagnetic waves.The focus of electromagnetic theory is initial boundary-value and boundary-value problems for the Maxwell equations. Those are the assumed models, from which, by applying mathematical methods, we should extract physical results. The modern computer-aided research process can be divided into several stages: qualitative mathematical analysis of the initial problem; the development of algorithms and implementation of the problem in software; problem-oriented computational experiments; and physical interpretation of the results. The success of the study depends in many aspects on whether sufficiently high standards of investigation can be maintained at all these stages and whether there is an 'intellectual core' in these investigations which enables us to gain new scientific knowledge [1]. As an example of a successful implementation of such an approach that has settled a long-standing conflict between theory and experiment, we can cite the development of the theory of resonant wave scattering in the frequency domain. These results have been reported (see for example, [2]-[16] and the bibliographies contained in those references), and they have served as a basis for the development of a number of essentially new functional units and devices in millimeter and sub millimeter radio-engineering, vacuum electronics and solid-state electronics, optics and spectroscopy.The modern theory of transient electromagnetic fields is still lacking achievements that may be compared with those existing in the frequency domain, neither by the profoundness of the study, nor by the intensity of the study of electromagnetic phenomena and, as a result by their applications. However, the process of accumulation of potentialities for a break through is a process still in action. Our activity now is devoted to just these problems; for the most part it is focused on the development and implementation of robust and efficient mathematical models for transient electromagnetic theory.The content of this paper has been partially inspired by the statement from [17]: "Therefore, it becomes clear that the boundary conditions are an integral part of a PDE (partial-differential-equation) problem, and should always accompany the FDTD (finite-difference time-domain) formulation of it. This inflicts particular concerns when the problem under examination is so-called 'open' space or unbounded problem, e.g., radiating, scattering, etc., meaning that the domain of interest is unbounded in one or more spatial-coordinate directions. For such problems, there are no exact boundary conditions known".However, exact 'absorbing' conditions (or 'fully absorbing' conditions) providing efficient limitation of the computational domain of finite-difference methods do exist now, since some time back. They have already taken their proper place in electromagnetic simulation in fundamental and ap...

show abstract

A difference scheme for the non-stationary maxwell equations in waveguide systems

Cited by 4 publications

References 2 publications

Time domain theory of open waveguide resonators: Canonical problems and a generalized matrix technique

Time domain theory of open waveguide resonators: Canonical problems and a generalized matrix technique

The Exact Absorbing Conditions Method in the Analysis of Open Electrodynamic Structures: Circular and Coaxial Waveguides

`Fully Absorbing' Boundary Conditions in the `Open' Electrodynamic Problems for Pulsed Waves

Contact Info

Product

Resources

About