JIN, J.: "The Finite Element Method in Electromagnetics", (John Wiley & Sons, Inc., New York, 1993).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....been well developed. Those methods include finite difference methods [7] 12] finite volume methods [6] 9] 13] and finite element methods [3] However, for many real applications, such as aerospace design and target identification, one needs to solve Maxwell s equations in inhomogeneous media [4] [7] 11] The aforementioned numerical methods are either not directly applicable or inefficient (with lower order convergence) for these problems due to different physical characteristics reflected by the electric permittivities and magnetic permeabilities of different media, and the extra ....

J. Jin. The finite element method in electromagnetics. John Wiley and Sons, Inc.

...., 1 ) 1 ( 4 3 # # = N ,and ) 1 ) 1 ( 4 4 # # = N With the coordinate transformation given in (A1 ) the n quadrilateral is transformed into a square with sides equal to 2, as shown in Figure 3. The vector basis function i N along the edges of the quadrilateral can be shown to be [ 6] # # # = 1 ( # # # = 1 ( # # # = 1 ( # # # = 1 ( If n is the unit normal vector to the n quadrilateral, then the basis function representing the surface current can be written as # # # # # = n l B n ) 1 ( 4 # # # # # = n l B n ) 1 ( 4 # # # # ....

.... then the basis function representing the surface current can be written as # # # # # = n l B n ) 1 ( 4 # # # # # = n l B n ) 1 ( 4 # # # # # = n l B n ) 1 ( 4 # # # # # = n l B n ) 1 ( 4 where the various quantities appearing in the above expressions can be expressed as [6 ] ] det[ J x y y # # # = # , det[ J x y y # # # = # (A5) # # # # # # # # # # # # y x y x J det[ A6) With simple mathematical manipulation it can be shown that ] det[ 1 4 l B ni = # # # 30 ....

J.Jin,"The finite element method in electromagnetics, " John Wiley & Sons, Inc., New York, 1993.

.... by unions of small rectangular, where as the region II is approximated by a union of triangular elements as shown in Figure 1(b) Expression (3) is valid for expressing the transverse electric field in the region II, where as the transverse electric field in the region I is expressed as [2] (5) where ) y x W is the vector basis function for the edge of a rectangular element in the region I. Using (3) and (5) the global matrices [ S and [ S can be obtained and the 4 r eigenvalues of rectangular waveguide can be obtained as a function of number of triangles ....

J. Jin, " The Finite Element Method in Electromagnetics, " John Wiley & Sons, Inc., New York, 1993.

.... i and i are constant functions i , i = 1; 2, but with possibly great differences in their values. We remark that our subsequent analyses can be naturally extended to the case with piecewise smooth coefficients as well as multiple subdomains for which our methods have broad applications [3, 14]. Let Gamma = 1 be the boundary 1 with a unit outward normal vector m, and let be the boundary of Omega with a unit outward normal vector n, see Figure 1. We supplement the system (1.1) 1.4) with the perfect conductor boundary condition and the initial condition given by E Theta n = 0 ....

....addition, we have the following constitutive relations D = E ; B = H ; 1.9) where D and B are the electric flux density and the magnetic flux density respectively. Over the past few decades, numerical methods for solving the Maxwell s equations in homogeneous media have received much attention [14, 24]. The simple and popular Yee s scheme was proposed in 1966 [25] though its convergence analysis was not available until the work by Monk and Suli for nonuniform rectangular grids [18] In order to handle domains with complicated geometry, both finite element and finite volume methods have been ....

J. Jin. The finite element method in electromagnetics. John Wiley and Sons, Inc.

....point to its neighbors but ours is defined in the middle of a cell face. The advantages of our approach are most evident when the methods are applied on extremely rough grids, especially when the properties of the media are discontinuous. The finite element method (FEM) see, for example, [18, 40], and the references therein) have been used extensively to solve Maxwell s equations. From our perspective the main difference between our FDM and FEMs is that in defining our discretizations we have built the discrete analogs of the continuous operators directly into the FDMs so they can be ....

J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 1993).

....The method robustness is demonstrated on a test model problem. Keywords: vector potential, Maxwell s equations, solution discontinuities, mixed finite elements, Krylov subspace methods, preconditioning. 1 Introduction Magnetostatic simulation is important and has many applications [2, 18, 20, 17]. In geophysics, this simulation is important in order to simulate the response of unexploded ordnances (UXO s) 5] and for the MMR experiment [18] In the UXO problem one needs to simulate the response of metal with permeability of roughly = 5 Theta 10 2 0 in a medium of = 0 and therefore ....

....for its solution in the case of large discontinuities are important. The problem evolves from Maxwell s equations in the static limit ( t( 0) which can be written as r Theta E = 0 (1a) r Theta H Gamma oeE = J s (1b) r Delta (H) 0 (1c) with appropriate boundary conditions on H (see [17]) In this paper we assume only Dirichlet type BC i.e. n Theta H) Omega = 0: There are two different magnetostatic problems. First, if the source is divergence free (such as the earth s magnetic field) i.e. r Delta J s = 0 then, it is easy to see that E = 0 and the system reduces to r ....

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J. Jin, The Finite Element Method in Electromagnetics, John Wiley and Sons, 1993.

....element discretization. Considerations of the first two problems mentioned above have lead to a widespread adoption of edge finite elements [6,7] for the discretization of the timeharmonic Maxwell s equations. For an engineering view of such elements, a good summary is contained in the books [8,9]. An error analysis of these elements has been given in [10 12] and the profound connection between these elements and differential forms has been noted for example in [13 15] Perhaps the main problem with such elements is that they become rather complex as the order of the elements is ....

J.-M. Jin, The finite element method in electromagnetics, Wiley, 1993.

.... simulating the electric potentials from neuronal activity in the brain as measured by electroencephalography (EEG) and the resulting external magnetic elds as measured by magnetoencephalography (MEG) The corresponding source model usually assumes that neurons act as current electric dipoles [2] such that the EEG and MEG forward problems can be reduced to closed form analytic solutions. With more realistic, inhomogeneous, anisotropic, non spherical head models, however, a closed form solution is not as easily computed and approximations, such as nite element methods, must be used. The ....

....head models, however, a closed form solution is not as easily computed and approximations, such as nite element methods, must be used. The simplest numeric nite element method employs linear basis functions to approximate the physical equations governing the electric and magnetic elds [2, 4, 7] and uses a constant electric gradient within an element. In contrast, a closer approximation of the physical equations and a non constant electric gradient within an element [1, 3, 9] may be made by using a higher order nite element method. As an initial part of understanding the accuracy and ....

Jin, J. The Finite Element Method in Electromagnetics. John Wiley & Sons, Inc., 1993.

....only within the domain constituted by a small number of adjacent cells. A class of shape functions, which complies with all the requirements listed so far, is that of the so called edge elements. These are shape functions, which were introduced some twenty years ago in finite element practice [Jin, 1993; Albanese and Rubinacci, 1998] Edge elements are usually defined in terms of the kind of interelement discontinuities they permit. Here, we will offer instead the following definition: an edge element is a shape function s p defined in a domain subdivided by a cell complex, whose projection on ....

....(290) mixes inextricably the two time dependent Maxwell s equations and the constitutive equations. The same holds true for the other approach to time dependent problems that preserves to the problem the ellipticity suited to the classical FE approach, that which considers time harmonic fields [Jin, 1993]. In that case Equation (290) becomes curl # 1 curlE # w 2 eE jswE jwJ i = 0 (293) where not only are the equations mixed, but the possibility of a space time approach is also definitely lost. Thus it seems that in spite of its physical origin, the classical FE approach is not capable ....

Jin, J. (1993). The Finite Element Method in Electromagnetics, Wiley, New York.

....in the anticipation that the inaccuracies of the traditional approach can be avoided. Edge element basis functions have desirable properties: they are divergence free but not curl free. They have been successfully used in finite element solutions to electromagnetic forward modelling (e.g. Jin, 1993). The use of similarly sophisticated, although di#erent, basis functions has been presented by Slob van den Berg (1995) We start by re deriving the form of the integral equation upon which our numerical solution is based, a form that reduces at zero frequency to the integral equation for the DC ....

....element basis vectors It is assumed that the region of anomalous conductivity can be represented by a grid of cuboidal cells within each of which the conductivity is constant. Within a cell, we approximate the x component of the total electric field by the linear combination of the four functions (Jin 1993): y y c l y ) z z c l z ) 4ly l z , 25) y c l y y) z z c l z ) 4ly l z , 26) y y c l y ) z c l z z) 4ly l z , 27) y c l y y) z c l z z) 4ly l z , 28) An integral equation solution for 3D EM modelling where y c and z c are the y and z coordinates of the ....

Jin, J., 1993, The Finite Element Method in Electromagnetics: John Wiley, New York.

.... while it is widely agreed that electromagnetic phenomena are generally governed by Maxwell s equations, the choice of numerical techniques to solve these equations depends on parameter ranges and various other restrictive assumptions, and as such is to a significant degree application dependent [20, 32, 2]. The present article is motivated by remote sensing inverse problems, e.g. in geophysics, where one seeks to recover material properties especially conductivity in an isotropic but heterogeneous body, based on measurements of electric and magnetic fields on or near the earth s surface. The ....

....in the ensuing discretization. The major departure from our previous work is in the fact that the identity (7) does not directly extend for the operator r Theta ( Gamma1 r Theta ) appearing in (5) We can, however, stabilize this operator by subtracting r( Gamma1 r Delta ) see, e.g. [20]) and this forms the basis for our proposed method. In cases of constant magnetic permeability or electric conductivity the formulation can be reduced to our previous formulation in [15] or a variant thereof. Our approach to dealing with possible discontinuities can be viewed as using fluxes ....

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J. Jin. The Finite Element Method in Electromagnetics. John Wiley and Sons, 1993.

....problem has been chosen for its high flexibility for the geometric modeling, in particular with strong variations of the scale of structural details. For the solution of Maxwell eigenvalue problems Kikuchi [2] suggested a mixed formulation method based on Nedelec s edge elements [3, 4] for the electric field and node based elements for the Lagrange multiplier. In this way, the computed approximate eigenmodes are naturally split into (physically meaningless) curl free and (in a discrete sense) divergence free modes. Spurious modes cannot appear. In the engineering literature the ....

J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 1993).

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J. M. Jin, The Finite Element Method in Electromagnetics. New York: John Wiley & Sons, 1993. 12 FIGURE CAPTIONS

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JIN, J.: "The Finite Element Method in Electromagnetics", (John Wiley & Sons, Inc., New York, 1993).

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Jian-Ming Jin. The Finite Element Method in Electromagnetics.Wi- ley, New York, 1993.

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J. M. Jin. The Finite Element Method in Electromagnetics. Wiley, New York, 1993.

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J. Jin, The Finite Element Method in Electromagnetics, New York: Wiley, 1993.

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Jin, J, The Finite Element Method in Electromagnetics John Wiley and Sons, 1993.

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J. Jin. The Finite Element Method in Electromagnetics. John Wiley & Sons, Inc., 1993.

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J. Jin. The Finite Element Method in Electromagnetics. John Wiley & Sons, Inc., 1993.

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J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 1993).

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Jin, Jianming. The Finite Element Method in Electromagnetics John Wiley and Sons, 1993.

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Jin, J, The Finite Element Method in Electromagnetics John Wiley and Sons, 1993.

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J. Jin. The Finite Element Method in Electromagnetics. Wiley, New York, 1993.

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J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 1993)

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