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T3P
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is
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a
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3D
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parallel
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finite-element
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time-domain
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solver
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to
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calculate
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transient
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field
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response
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of
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a
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electromagnetic
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structure
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to
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imposed
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fields,
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and
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dipole
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or
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beam
...
excitations.
In our approach, Ampere's and Faraday's laws are combined and integrated over time to yield the inhomogeneous vector wave equation for the time integral of the electric field E:
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\begin{eqnarray*} |
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\left( \epsilon \frac{\partial^2}{\partial t^2} + \sigma_{eff} \frac{\partial}{\partial t} + \nabla \times \mu^{-1}\nabla\times \right) \int^t \emph{E} d \tau = -\emph{J} \end{eqnarray*} |
with permittivity
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$\epsilon = \epsilon_0 \epsilon_r $ |
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$\mu = \mu_0 \mu_r$
|
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$\sigma_{eff} = \tan \delta \cdot 2 \pi f \cdot \epsilon $ |
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$f$ |
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$\tan \delta $ |
The computational domain is discretized into curved tetrahedral elements and
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$\int^t \emph{E}d \tau $ |
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$ \emph{N}_i (x) $ |
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\begin{eqnarray*} \int^t \emph{E} (\emph{x}, \tau) d \tau = \sum^{N_p}_{i=1} e_i (t) \cdot \emph{N}_i (x) \end{eqnarray*} |
up to order
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$p$ |
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$N_1 = 6 $ |
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$N_2 = 20 $ |
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$N_6 = 216 $ |