The supplied total current in the inductor wire is considered by the following condition for
:
where
is an arbitrary closed loop around the conducting wire,
is the
number of edges, which build this loop, and
is the length of the
-th loop edge.
The Dirichlet boundary part from (5.27) is expressed as
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Only the supply parts of the wire, which are used to force the electric current, lie directly on
the outer bound of the simulation domain. The remaining parts of the wire are surrounded
by dielectric material. The loop
is chosen to lie on the outer face of
the simulation domain. The Neumann boundary
consists of all edges lying on
the outer boundary of the simulation domain excluding the edges building
.
In this work the dielectric environment enclosing the wire is assumed to be
sufficiently thick so that
can be neglected on the dielectric part of
.
On the other hand the electric current density is forced in a direction
perpendicular to the conductor boundary faces. Thus, for isotropic materials with respect to
,
will be also perpendicular to these faces and the homogeneous Neumann boundary
condition (5.30) is used for the conductor surface parts.
For the calculations of
it is sufficient
that one node of the simulation domain is
set to an arbitrary value. Thus, the Dirichlet boundary part of
(5.27) is modified to read
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(6.25) |
The Neumann boundary
consists of all edges lying on the outer boundary
of the simulation domain.
The simulation domain is constructed sufficiently large to allow that the magnetic flux
can be
neglected on the outer boundary
. Thus the homogeneous Neumann boundary condition
(5.32) is applied.