电磁场数值分析(西电)

Electromagnetic theory
Functional and matrix
Method of moment (MoM) （矩量法）
Finite element method (FEM) （有限元法）
Finite-difference time-domain methods （时域有限差分方法）
(1.12)
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Volumetric equivalence principle for penetrable scatterers (I)
Differential equations Integral equations
To simplify the formulation of integral equations
a heterogeneous space
volumetric equivalence principle
However, the equivalent sources are unknowns to be determined.
The derivatives in (1.19)and (1.20) must be interpreted in the context of generalized functions.
1 2 E k rE 0 r 2 1 H k rH 0 r
(1.9)
(1.10)
where k 2 2 0 0 ,the parameter k is known as the wavenumber of the medium.
Convert the original problem into an equivalent problem
Replace the inhomogeneous dielectric and magnetic material present in the problem by equivalent induced polarization current and charges.
12
(1.17) (1.18) (1.19) (1.20)
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Volumetric equivalence principle for penetrable scatterers (III)
Equations (1.13)-(1.16)
a homogeneous space
Equations (1.1)-(1.4)
-1Computational methods for electromagnetics
（电磁场数值分析）
Xie, Yongjun家（谢拥军） Department of Microwave Telecommunication Engineering
1
Outline of this class
Basis for the computational methods
(1.14) (1.15)


(1.16)
K j0 r 1H J j0 r 1E 1 e 0 r E r 1 m 0 r H r
where
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Volumetric equivalence principle for penetrable scatterers (II)
E j0H K H j0 E J 0 E e
0 H m
(1.13)
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Conclusions
• About thjs class
• Maxwell’s equations and boundary conditions
• Vector Helmholtz equations • Two-dimensional problems and the scalar Helmholtz equations • Volumetric equivalence principle
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Two-dimensional problems and the scalar Helmholtz equations (I)
Two-dimension al problems are those with invariance in the third dimension,such as an infinite cylindrical structure illuminated by a field that does not vary along the axis of the cylinder. Usually the cylinder axis lies along the z axis in a Cartesian coordinate system. ˆ
It is convenient to separate the fields into transverse magnetic (TM) and transverse electric (TE) parts with respect to the variable z. The ˆ z-component of the magnetic field is absent in the TM case, while the ˆ z -component of the electric field is absent in the TE case.
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Two-dimensional problems and the scalar Helmholtz equations (II)
Under the assumption of the z-invariance, the z-component of Equation (1.9) can be extracted and written in the form of a scalar Helmholtz equation
1 2 Ez k r Ez 0 r
Similarly, we have
TM part of the field
Байду номын сангаас
(1.11)
1 2 H z k H z 0 r
TE part of the field
3
An inhomogeneity illuminated by an incident electromagnetic field
0
0
0 r
inc E
0 r
s E
ˆ k
inc H
Hs
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Boundary conditions
Regions containing penetrable dielectric or magnetic material may be bounded by material having a very conductivity, which is often approximated by infinite conductivity and termed a perfect electric conductor. n is the normal vector to the surface that points into the ˆ the problem domain, J s is the surface current density, and s is the surface charge density.
2
Maxwell’s equations
E j0r H H j0 r E
(1.1) (1.2) (1.3) (1.4)
0r H 0
0 r E 0




source-free region with relative permittivity r and permeability r Have specialized that the medium is linear and isotropic and j t the electromagnetic field has time dependence e
ˆ nE 0 ˆ n H Js s ˆ nE 0 r
(1.5) (1.6) (1.7) (1.8)
ˆ nH 0
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Vector Helmholtz equations
By combining equations (1.1) and (1.2) and eliminating one of the fields, we obtain the “curl-curl” form of the vector Helmholtz equations