March 2014
Intermediate
876 pages
28h 17m
English
Content preview from The Finite Element Method in Electromagnetics, 3rd Edition
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CHAPTER 12FINITE ELEMENT ANALYSIS IN THE TIME DOMAIN
All the finite element analyses of electromagnetic field problems we have covered so far were carried out in the frequency domain. Analyzing electromagnetic fields in the frequency domain has been a common practice in electromagnetics because solving Maxwell’s equations in the frequency domain represents a mathematical problem in three dimensions, whereas dealing with them directly in the time domain is a much more challenging four-dimensional problem. Although it seems that a frequency-domain solution is valid only for time-harmonic fields at a single frequency, a frequency-domain analysis can actually be used to solve general transient electromagnetic problems with the aid of the Fourier transform. Given an arbitrary transient source, we can first compute its Fourier transform, sample it at a number of frequencies, then solve for the time-harmonic fields at the sampled frequencies, and finally find the transient fields via the inverse Fourier transform. The price to pay is to repeat the frequency-domain analysis at many frequencies.
Whereas most electromagnetic problems can be dealt with using a frequency-domain method, in some applications solving Maxwell’s equations directly in the time domain can offer some important advantages. For example, by designing a proper source, a time-domain analysis can yield the solution to a problem over the entire frequency band of interest without requiring repetition of the analysis at ...
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