Sadiku的《数值电磁学方法(第二版)》：研究生电磁学课程权威教材

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"Numerical Techniques in Electromagnetics, 第二版，由 Matthew N. O. Sadiku 博士编著，是 CRC Press 出版的一本专为研究生级别的电磁学计算课程设计的权威教材。这本书详细探讨了数值分析在电磁学领域的应用，涵盖了广泛的理论和技术，包括但不限于有限差分法、有限元方法、傅里叶变换和谱分析等。书中内容基于严谨的科学原理和实践案例，旨在帮助读者理解和掌握电磁场问题的数值求解方法。本书的特点在于其深度与广度兼备，不仅介绍了基本的数值技术，还涉及了高级的模拟和优化技术。它包含了许多来自被高度评价的来源的信息，其中的部分内容是经过授权重印的，并且对引用资料进行了明确标注。书中提供了丰富的参考文献，鼓励读者进一步探索相关领域。然而，由于版权原因，未经出版商事先书面许可，任何形式的复制或传播，如复印、微缩摄影、录音以及通过信息存储或检索系统，均需遵循严格的限制。CRC Press LLC 不授予一般性的复制或推广许可，除非特别获得书面许可，否则不得用于创作新作品或商业销售。如果你对本书的内容有兴趣或者需要获取更多的许可信息，可以直接联系 CRC Press LLC，地址位于 2000 N.W. Corporation Drive。Numerical Techniques in Electromagnetics 是一本极具价值的工具书，对于电磁学研究者、工程师和学生来说，是深入理解并实践电磁场计算的重要参考资料。"

theorem,



F · dS =



∇·F dv (1.1)

and Stokes’s theorem



F · dl =



∇×F · dS (1.2)

Perhaps the best way to review EM theory is by using the fundamental concept of

electric charge. EM theory can be regarded as the study of ﬁelds produced by electric

charges at rest and in motion. Electrostatic ﬁelds are usually produced by static

electric charges, whereas magnetostatic ﬁelds are due to motion of electric charges

with uniform velocity (direct current). Dynamic or time-varying ﬁelds are usually

due to accelerated charges or time-varying currents.

1.2.1 Electrostatic Fields

The two fundamental laws governing these electrostatic ﬁelds are Gauss’s law,



D · dS =



dv (1.3)

which is a direct consequence of Coulomb’s force law, and the law describing elec-

trostatic ﬁelds as conservative,



E ·dl = 0 (1.4)

In Eqs. (1.3) and (1.4), D is the electric ﬂux density (in coulombs/meter

), ρ

is the

volume charge density (in coulombs/meter

), and E is the electric ﬁeld intensity (in

volts/meter). The integral form of the laws in Eqs. (1.3) and (1.4) can be expressed

in the differential form by applying Eq. (1.1) to Eq. (1.3) and Eq. (1.2) to Eq. (1.4).

We obtain

∇·D = ρ

(1.5)

and

∇×E = 0 (1.6)

The vector ﬁelds D and E are related as

D = E (1.7)

where  is the dielectric permittivity (in farads/meter) of the medium. In terms of the

electric potential V (in volts), E is expressed as

E =−∇V (1.8)

1.2.4 Boundary Conditions

The material medium in which an EM ﬁeld exists is usually characterized by its

constitutive parameters σ, , and µ. The medium is said to be linear if σ, , and µ

are independent of E and H or nonlinear otherwise. It is homogeneous if σ, , and

µ are not functions of space variables or inhomogeneous otherwise. It is isotropic if

σ, , and µ are independent of direction (scalars) or anisotropic otherwise.

Figure 1.1

Interface between two media.

The boundary conditions at the interface separating two different media 1 and 2,

with parameters (σ

,

,µ

) and (σ

,

,µ

) as shown in Fig. 1.1, are easily derived

from the integral form of Maxwell’s equations. They are

= E

(

− E

)

× a

n12

= 0 (1.27a)

− H

= K or

(

− H

)

× a

n12

= K (1.27b)

− D

= ρ

(

− D

)

· a

n12

= ρ

(1.27c)

− B

= 0or

(

− B

)

· a

n12

= 0 (1.27d)

where a

n12

is a unit normal vector directed from medium 1 to medium 2, subscripts

1 and 2 denote ﬁelds in regions 1 and 2, and subscripts t and n, respectively, denote

tangent and normal components of the ﬁelds. Equations (1.27a) and (1.27d) state

that the tangential components of E and the normal components of B are continuous

across the boundary. Equation (1.27b) states that the tangential component of H is

discontinuous by the surface current density K on the boundary. Equation (1.27c)

states that the discontinuity in the normal component of D is the same as the surface

charge density ρ

on the boundary.

In practice, only two of Maxwell’s equations are used (Eqs. (1.22c) and (1.22d))

when a medium is source-free (J = 0,ρ

= 0), since the other two are implied (see

Problem 1.3). Also, in practice, it is sufﬁcient to make the tangential components

of the ﬁelds satisfy the necessary boundary conditions since the normal components

implicitly satisfy their corresponding boundary conditions.

1.2.5 Wave Equations

As mentioned earlier, Maxwell’s equations are coupled ﬁrst-order differential equa-

tions which are difﬁcult to apply when solving boundary-value problems. The difﬁ-

culty is overcome by decoupling the ﬁrst-order equations, thereby obtaining the wave

equation, a second-order differential equation which is useful for solving problems.

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Sadiku的《数值电磁学方法(第二版)》：研究生电磁学课程权威教材

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