C hapter t refethen the diculties caused b y b oundary conditions in scien ti c computing w ould be hard to o v eremphasize boundary conditions can easily mak e the. Kaganovab, a triniti, 142092 troitsk, moscow reoion, russia b institute for hioh pressure physics russian academy of sciences 142 092 troitsk, moscow region, russia abstract under the conditions of the normal m,omalous skineffect the effective surface impedance. The main purpose of this paper is to show the analyticity, of the solution to the maxwell system with the boundary condition 2, with respect to k. If the surface of an inhomogeneous metal is flat, the effective surface impedance associated with the reflection of an averaged electromagnetic wave is equal to the value of the local impedance tensor averaged over the surface inhomogeneities. Having in mind to calculate the leading terms in the expressions for the elements of the effective impedance tensor, in our calculations we use lbc. Leontovich boundary condition from the scattering data at one frequency and one incident direction is already known 7. High order surface impedance boundary conditions with the.
The limiting behavior of the unique solution to the scattering problem for the maxwell equations with a leontovich boundary condition in an inhomogeneous medium as the impedance goes to zero is inv. The resulting eigenproblem is linearized through an eigenvalue transformation and solved using the arnoldi algorithm. Impedance boundary conditions in a hybrid femmom formulation. In 1946 leontovich and fock2 applied the pe method to the problem of transhorizon radio wave propagation above a spherical earth, thereby making a breakthrough in electromagnetic wave propagation modeling. Approximately 30 years passed before a practical algorithm for solving the leontovichfock parabolic wave equation was developed.
This boundary condition is applied in geophysics for sounding of the lithosphere and diagnostics of the magnetosphere by electromagnetic waves. Kaganovab, a triniti, 142092 troitsk, moscow reoion, russia b institute for hioh pressure physics russian academy of sciences 142 092 troitsk, moscow region, russia abstract under the conditions of the normal m,omalous skineffect the effective surface. Often they are called the leontovich boundary conditions lbc. The question of what boundary conditions are satisfied by an electromagnetic field has been touched upon in the mathematics literature a number of times since the work by leontovich in the early 1940s, see, in relation to wave propagation near the surface of the earth. Scattering of maxwells equations with a leontovich boundary. Surface impedance absorbing boundary for terminating. We will consider boundary conditions that are dirichlet, neumann, or robin. However, there is evidence that leontovich has actually come to the idea of approximate boundary conditions at the end of the thirties, at the same time as schukin.
Approximately 30 years passed before a practical algorithm for solving the leontovich fock parabolic wave equation was developed. Leontovich boundary conditions in case of the pointlike charge passing along the axis of the cylindrical vacuum channel lined with dielectric 14. Imperfectly conducting closedshaped, convex and smooth body, for which the following inverse boundary conditions are derived from the leontovich direct boundary condition eh. The use of the leontovich condition is shown to open new possibilities for investigating the anharmonicity of mhd oscillations of. Suitable impedance boundary condition applied to the. Applying periodic boundary conditions in finite element. Leontovichs impedance boundary conditions can be applied. This paper discusses the general issues, derivation, implementation and applications of surface impedance boundary conditions sibcs in the time and frequencydomains.
Application of leontovich boundary conditions ensures proper solution at the change of media and its low computational cost permits acceleration of predictions. The leontovich boundary condition is a classical electrodynamics boundary condition that relates to the tangential components of the electric e t and magnetic h t fields on the surface of wellconducting bodies. In hypermesh, boundary conditions are stored within what are called load collectors. Pages in category boundary conditions the following 16 pages are in this category, out of 16 total. On the concept of vector polarization electromagnetic. On the leontovich boundary condition in geoelectromagnetism. These waves have much in common with the rayleigh waves in elasticity theory. The results are important in showing the effect of surface curvature and material variations, and we will now apply the same method to the formulation used by leontovich 1948. Since then, surface impedance boundary conditions have seen a steady increase in applications and acceptance and the development of new types and new methods of computation.
Finite element based eigenanalysis for the study of. The leontovich boundary conditions and calculation of. On the leontovich boundary condition in geoelectromagnetism article pdf available in izvestiya physics of the solid earth 459. Index termsasymptotic diffraction theory, boundary value problems, conducting materials, higherorder boundary conditions, impedance boundary conditions ibcs. Morozov, who also estimated the errors that arise when these conditions are used to determine the field of a moving charge. Leontovich published his results without derivation later, in 1944 4. Surface impedance absorbing boundary for terminating fdtd. The use of the leontovich condition is shown to open new possibilities for investigating the anharmonicity of mhd oscillations of the. According to leontovich, at the surface on the lossy conductor the electric and magnetic fields are related by e.
Impedance boundary conditions in a hybrid femmom formulation hao wang, minjia xu, member, ieee, chen wang, student member, ieee, and todd hubing, senior member, ieee abstract when numerically modeling structures with imperfect conductors or conductors coated with a dielectric material, impedance boundary conditions ibcs can substantially. Frequencydependent impedance and surface waves on the. High order surface impedance boundary conditions with the a. Pdf on the 70th anniversary of the leontovich boundary. Oct 16, 2003 if the surface of an inhomogeneous metal is flat, the effective surface impedance associated with the reflection of an averaged electromagnetic wave is equal to the value of the local impedance tensor averaged over the surface inhomogeneities. The boundary conditions obtained senior, 1990 are more general than those given by either author, and reveal some errors in the expressions quoted by leontovich. On the 70th anniversary of the leontovich boundary condition. However, the approach to surface impedance boundary conditions has been ad hoc, and almost entirely dependent on the leontovich condition which is a. To address the excessive computational requirements of this approach and to achieve a. On the 70th anniversary of the leontovich boundary. The mathematical expressions of four common boundary conditions are described below. We compare here the previously obtained solution with those that could be derived with the help of the leontovich boundary conditions, formula 6 by applying recently proposed integral theorem.
During the past thirty years, researchers have applied surface impedance concepts in the frequency domain to numerous electromagnetic scattering problems. Load collectors may be created using the right click context menu in the model browser create load collector. Eigenanalysis of electromagnetic structures based on the. Doubt is cast on the assertion by alshits and lyubimov usp. The first rigorous mathematical analysis was done by rytov 8. The use of the leontovich boundary conditions in cerenkov radiation theory was first proposed by a. Of historical interest, surface impedance boundary conditions were first proposed by leontovich in the 1940 s 6 and were rigorously developed by senior in 1960 7. With this paper, we demonstrate that the same integral relation that we call relativistic gauss theorem can be applied in case impedance boundary conditions ibc also known as leontovich boundary conditions. The paper is dedicated to the 70th anniversary of the formulation of the leontovich impedance boundary condition. Introduction impedance boundary conditions ibcs formulated by leontovich 1 laid the foundation for using and deriving approximate conditions in electromagnetics. Periodic boundary conditions pbc are a set of boundary conditions that can be used to simulate a large system i. The 1940 paper by rytov written on the suggestion of leontovich is indicated as evidence for the latters full awareness of exactly how accurate his proposed boundary condition was. The leontovich impedance boundary condition et zht n 1. Physlca elsevier physica a 241 1997 154160 on the effective leontovich boundary conditions for polycrystals a.
Analytical loss factors in approximation of the leontovich. A systematic approach to the concept of surface impedance. These two techniques are then combined to verify the measurement campaigns developed at metro tunnels during the thesis. Impedance boundary conditions and effective surface impedance. The question of leontovichs 70year old boundary condition at the surface of a well conducting body is discussed. In the paper, the ray theory of this electromagnetic analog of the rayleigh waves is constructed. In 1992, maloney 8 and john beggs 9 both successfully implemented leontovichs surface impedance boundary condition with fdtd method, but not as an absorbing boundary. Dirichlet boundary conditions specify the aluev of u at the endpoints. Existence and uniqueness of solution to the direct. A systematic approach to the concept of surface impedance boundary conditions nathan ida, sergey yuferev, and luca di rienzo abstract.
The key is to combine known solution of the laplace equation in such a way as to satisfy the k. Since then, surface impedance boundary conditions have seen a steady increase in applications and acceptance and the development of. Boundary conditions when a diffusing cloud encounters a boundary, its further evolution is affected by the condition of the boundary. Leontovich has been developed in an attempt to simplify the analysis of propagation of electromagnetic waves over the surface of the earth 2. This result is exact within the accuracy of the leontovich boundary conditions. A methodology of evaluating losses effects and particularly the quality fac tors within practical accuracies by just solving the linear eigenproblem resulting from perfect electric boundary conditions is devised by our group 3. On the effective leontovich boundary conditions for. Pbc has been favored among many researchers and practicing engineers in the study of various materials. The question of leontovich s 70year old boundary condition at the surface of a well conducting body is discussed. As originally formulated by russian physicist mikhail leontovich, the boundary condition is given as.
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