# Advanced Modeling in Computational Electromagnetic by Dragan Poljak

By Dragan Poljak

This article combines the basics of electromagnetics with numerical modeling to take on a extensive diversity of present electromagnetic compatibility (EMC) difficulties, together with issues of lightning, transmission strains, and grounding structures. It units forth an exceptional starting place within the fundamentals prior to advancing to really expert issues, and permits readers to improve their very own EMC computational versions for purposes in either study and undefined.

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88) is homogeneous, while its electric counterpart implies the important fact that all electromagnetic phenomena are due to electric charges. 89) are valid for uniform regions and represent a signiﬁcant degree of mathematical simpliﬁcation as compared to the Maxwell equations. Many practical problems can be handled by solving one wave equation without reference to the other, so that only a single boundary-value problem in a single vector variable remains. 91) are the equation of motion of electromagnetic waves in free space.

The magnetic vector potential may be derived following a similar treatment. 171) is carried out by separating this vector equation into its Cartesian components. The result is a set of equations identical in form to the scalar potential equation. 171). 13 GENERAL BOUNDARY CONDITIONS AND UNIQUENESS THEOREM For the realistic problem under consideration, the boundary qV of a problem domain V is generally composed of three distinct boundary segments qD, qN, and qC. Now, let the solution u (representing electric scalar potential, magnetic vector potential, electric ﬁeld, or magnetic ﬁeld) satisfy the following conditions on the three segments: u ¼ u0 on qD ðDirichletÞ ð2:172Þ qu ¼ q0 qn on qN ðNeumannÞ ð2:173Þ on qCðCauchyÞ ð2:174Þ qu þ au ¼ p0 qn The Dirichlet conditions are called essential or principal boundary conditions, whereas the Neumann boundary conditions are called natural boundary conditions.

Namely, the right-hand side represents a time-varying point charge. 167) is that the potential still corresponds to the charge causing it, but with a time retardation which equals the time taken for light to propagate from the charge to the point of potential observation. The electrostatic potential, on the contrary may be viewed simply as the special case of very small retardation, that is, a simpliﬁcation valid at close distances. 167) can be applied to the more general case of time-varying charge distributed over some ﬁnite volume of space V by dividing the volume into small portions and treating the charge in each as a point charge at the given point.