By Reinhold Pregla
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Extra resources for Analysis of Electromagnetic Fields and Waves: The Method of Lines (RSP)
E. EB = 0. By using eq. e. y 1 = I , because tanh(Γd) approaches a unit matrix. 76) We assume that the electric ﬁeld is equal in the plane M on both sides of the strip. 77) From eq. 78) Now a further condition in the plane M must be introduced. The components of EM on the strip and the components of SM outside the strip must be zero. Therefore eq. 79) 35 basic principles of the method of lines The ﬁrst equation is an indirect eigenvalue problem, and the second one allows the determination of EM from SMS , the supervectors of the currents on the strip.
127) Iy◦ In the middle expression we have discarded those rows of Iy◦ which are also ◦ t rows of Iy2 . The matrices J•t , J✷t and J✸ can be constructed likewise. 128) The reduction of the interpolation matrices is done in an analogue way.
We assume that there is no variation in y-direction. The expression Dy = 0 is introduced into the z z operators [RE ] and [RH ] in eqs. 13). We see that the oﬀ-diagonal elements are zero. Therefore, we obtain two decoupled polarisations that can be treated independently. As usual in the MoL, the operators are now discretised with ﬁnite diﬀerences. The positions of the discretisation lines in a 2D-structure are shown in Fig. 8. As mentioned before, the fulﬁlment of the boundary conditions suggests determining the ﬁeld components on diﬀerent positions, which are shifted by half a discretisation distance.