电磁场数值分析谢拥军2

1、1-2-The description of a scattering problem Xie, Yongjun（谢拥军）Department of Microwave Telecommunication Engineering2Quick summary of last class (I)incEincHk00r0r0sEsH3Quick summary of last class (II)How to describe the electromagnetic problems?Maxwells equations and boundary conditionsVolumetric equi

2、valence principleThe inhomogenerous material can be replaced by equivalent induced sources radiating in free space4General description of a scattering problem (I)Splitting the fields into two partsOne associated with the primary source located somewhere outside the scattererAnother associated with t

3、he equivalent induced sourceIncident fieldsincEincHScattered fieldsssHE5General description of a scattering problem (II)The original fields in the presence of the scatterer can be written as:sincsincHHHEEE(2.1)(2.2)where002222incincincincHkHEkE(2.3)(2.4)00220022jKKjJHkHKjJJjEkEssss(2.5)(2.6)6General

4、 description of a scattering problem (III)Some additional explanations:(1) The vector Laplacian:EEE2(2.7)(2)our interests is the case of an excitation produced by some source in the far zone. Often, we will consider the incident field to be a uniform plane wave.(3) Radiation conditions in a three-di

5、mensional problemssrssrHjkHrEjkErlimlim(2.8)(2.9)where r is the conventional spherical coordinate variable.7General description of a scattering problem (IV)(4) Radiation conditions in a two-dimensional problemszszszszHjkHjkEElimlim(2.10)(2.11)(the Sommerfeld radiation conditions)For the TM and TE po

6、larizations, respectively, where is the radial variable in cylindrical coordinates.8Source-field relationships in homogeneous space - a first form (I)How to solve equations (2.5) and (2.6)?The classical approach is to express the fields in terms of the magnetic vector potential and the electric vect

7、or potential .according to AFFjAkAEs02(2.12)02jFkFAHs(2.13)And the vector potential satisfyKFkFJAkA2222(2.14）（2.15）9Source-field relationships in homogeneous space - a first form (II)The solution to equations (2.14)and (2.15) satisfying the radiation condition can be concisely written in the form GK

8、FGJA*(2.16)(2.17)where the scalar function G is the well-known three-dimensional Greens functionreGrjk4(2.18)And the asterisk (*)denote three-dimensional convolution, that is, rdrerJrArrjk4(2.19)10Source-field relationships in homogeneous space - a first form (III)The two-dimensional Greens function

9、 is kHjG2041(2.20)To summarize, the above procedure is the integration-followed-by-differentiation procedure, which is NOT well suited for numerical implementation.11Source-field relationships in homogeneous space - a second form (I)As an alternative to the pure vector potential source-field relatio

10、nship, a mixed-potential formulism can be developedmsesFjAHFAjE00(2.21)(2.22)where and are scalar potential functions and given byemGGmmee*00(2.23)(2.24)where the asterisk again denotes multidimensional convolution. 12Source-field relationships in homogeneous space - a third form (I)Using an analogy

11、 between Equations (2.14) and (2.15) and their general solutions ( 2.16) and (2.17)and vector Helmholtz equations appearing in (2.5) and (2.6). Formally, we can write the solutions to Equations (2.5) and (2.6) directly asGjKKjJHGKjJJjEss*0000(2.25)(2.26)A differentiation followed by an integration.1

12、3Source-field relationships in homogeneous space - a fourth form (I)A simple interchange of integration and differentiation results inmkmjsekejsGKGJHGKGJE*(2.27)(2.28)Where and are the dyadic Greens functions for the electric field, symbolically denotedGIGGIkjGekej201and and are the dyadic Greens functions for the magnetic field,GIkjGGIGmkmj201(2.29)(2.30)(2.31)(2.32)14Duality relationshipsPrinciple of Duality: the equations describing electromagnetic fields remain valid if all the quantities in the left