By Charles W. Steele
For good over a decade, the numerical method of box computation has been gaining gradually higher significance. Analytical tools offield compu tation are, at top, not able to house the very wide array of configura tions during which fields needs to be computed. nonetheless, numerical tools can accommodate many functional configurations that analytical equipment can't. With the arrival of high-speed electronic pcs, numerical box computations have ultimately turn into functional. in spite of the fact that, in an effort to enforce numerical equipment of box computation, we want algorithms, numerical tools, and mathematical instruments which are mostly particularly diverse from those who were normally used with analytical equipment. lots of those algorithms have, in truth, been awarded within the huge variety of papers which were released in this topic within the final 20 years. And to a couple of these who're already skilled within the artwork of numerical box computations, those papers, as well as their very own unique paintings, are sufficient to provide them the information that they should practice functional numerical box computations.
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Extra info for Numerical Computation of Electric and Magnetic Fields
It is essential to understand these effects very early in the computational process. Continuity conditions are discussed below for the electric field, the magnetic field, the electric and magnetic scalar potentials, and the magnetic vector potential. Each vector field is decomposed into a component tangential to the interface, subscripted t, and a component normal to the interface, subscripted n. The permittivity, permeability, and conductivity are all assumed to be isotropic. That is, D and J have the same direction as E, and B has the same direction as H.
Rectangular higher order shape function. we use Lagrange interpolating polynomials. 4. 6-3) where X k and YI are coordinates of interpolating points. Figure 4-9 shows a typical rectangular higher order shape function. 5. ISOPARAMETRIC SHAPE FUNCTIONS IN TWO DIMENSIONS All of the shape functions that have been formulated so far in this chapter have been functions of the spatial coordinates of the problem, the global coordinate system. As shown below, one can also use local, dimensionless isoparametric coordinates.
The condition that El is linearly polarized requires that Enl and Etl be in phase, and that En2 and Et2 be in phase. But this is not necessarily true. Therefore, in general, the electric field in the dynamic steady-state case is elliptically polarized, and angles of incidence cannot be defined. 1-13) The angle of incidence, 8, is defined as the angle that the field makes with a normal to the interface. 1-17) where 01 and O2 are the an~es of incidence if the electric field is on the medium # 1 side and the medium #2 side ofthe interface.
Numerical Computation of Electric and Magnetic Fields by Charles W. Steele