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6. Applications

In this chapter different applications using scalar and vector finite element methods are presented. The first application is used to evaluate the numerical analysis performed by the combination of a vector and scalar finite element method from Section 5.2. The magnetic field and the current density distribution in a coaxial structure are numerically calculated for the quasi-magnetostatic case as discussed in Subsection (5.1.3). As consequence the inductance and the resistance of the structure are obtained. These parameters are calculated also analytically, since the intentionally chosen coaxial structure provides analytical solutions for them. The analytical results agree very precisely with the numerical ones.

The second application handles a structure, for which no analytical or only rough formulas can be given, an on-chip spiral inductor. Its main properties for further electromagnetical analysis, the resistance and the inductance, are obtained numerically. The field distributions are visualized to show the plausibility of the used method.

The third application shows the simplification of the simulation of periodic structures by applying the so called periodic boundary conditions.



Subsections
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A. Nentchev: Numerical Analysis and Simulation in Microelectronics by Vector Finite Elements