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23 Chapter 3 – The Yee’s Finite-Difference Time-Domain (FDTD) Scheme for Maxwell’s Equations 3.1 Introduction In this chapter a brief introduction of the procedure for applying finite-difference time- domain (FDTD) method to time-domain Maxwell equations is shown. Specifically the Yee’s FDTD formulation will be illustrated. In this chapter the Yee FDTD scheme will be restricted to a model with linear, non-dispersive and non-magnetic dielectric. Various considerations such as numerical dispersion, stability of the model and terminating the model with absorbing boundary condition (ABC) will be discussed. Extension of the Yee FDTD scheme to a general printed circuit board (PCB) environment will be discussed in Chapter 4. A FDTD software to implement all the algorithms in Chapter 3 and 4 will be shown in Chapter 5 and a more general stability theorem will be presented in Chapter 6. 3.2 Maxwell’s Equations and Initial Value Problem Consider the general Maxwell’s equations in time domain including magnetic current density M r and magnetic charge density m ρ (Balanis 1989): B M E t r r r ∂ ∂ − − = × ∇ (3.2.1a) D J H t r r r ∂ ∂ + = × ∇ (3.2.1b) e D ρ = ⋅ ∇ r (3.2.1c) m B ρ = ⋅ ∇ r (3.2.1d) M r and m ρ are equivalent sources since no magnetic monopole has been discovered to the best of the author’s knowledge. The other parameters for (3.2.1a)-(3. 2.1d) are listed as follows: E r - Electric field intensity H r - Magnetic field intensity D r - Electric flux density
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