7. Equations of Electromagnetics

  1. Pavel Šolín

Published Online: 30 NOV 2005

DOI: 10.1002/0471764108.ch7

Partial Differential Equations and the Finite Element Method

Partial Differential Equations and the Finite Element Method

How to Cite

Šolín, P. (2005) Equations of Electromagnetics, in Partial Differential Equations and the Finite Element Method, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471764108.ch7

Publication History

  1. Published Online: 30 NOV 2005
  2. Published Print: 4 NOV 2005

ISBN Information

Print ISBN: 9780471720706

Online ISBN: 9780471764106

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Summary

Chapter 7 is a newcomer's introduction to computational electromagnetics. The first section introduces the quantities of the electromagnetic field and formulates their relations in the integral and differential form. Discussed are constitutive relations, media, conductors and dielectrics, magnetic materials and interface conditions. A separate section is devoted to potentials, since potential formulations usually can simplify the finite element solution of electromagnetics problems significantly. The time-harmonic Maxwell's equations are derived and the Helmholts equation is discussed. The time-harmonic Maxwell's equations are formulated in the weak sense and the existence and uniqueness of their solution is shown. Introduced are the lowest-order edge (Whitney) elements and the higher-order nodal edge elements of Nedelec. Discussed is the interpolation on these elements and their conformity to the Hilbert space H(curl). The standard steps in the discretization of the time-harmonic Maxwell's equations via the edge elements, such as the transformation os the weak forms to the reference domains and the design of suitable basis functions, are discussed in detail.