3.3 Box Integration Method
To overcome the limitations of the finite difference method the box integration method
[49, p.191] [50]^{3.1} can be used. The
simulation domain is partitioned into subdomains without overlap or exclusion. An example can
be seen in Fig. 3.3.
Figure 3.3:
A set of 13 grid points together with their associated VORONOI
regions which are bounded by the dashed lines.

The subdomains are also called VORONOI^{3.2} regions. A
VORONOI region is defined as the set of all points that are closer to the
considered grid point than to any other grid point. The differential equations are then
integrated over each of the subdomains and discretized by approximating the integrals by
numerical integration rules.
For an orthogonal grid structure the box integration method leads to the expressions obtained
from the finite difference method.
To get a connection between the global and the local attributes of fields, a
relation between the integral over a domain and the boundary of this domain
must be presented. Its general form is the GREEN transformation

(3.16) 
By reducing
to a vector
, the theorem of GAUSS is
obtained

(3.17) 
where
denotes the integration volume,
is
the boundary of the volume and
is the unity vector which is normal
to the boundary and points from the inside to the outside.
Subsections
M. Gritsch: Numerical Modeling of SilicononInsulator MOSFETs PDF