Applying the theorem of GAUSS to the left hand side turns eqn. (3.18) into

(3.19) |

The integrals are approximated as follows:

where is the projection of the flux onto the grid edge , evaluated at the midpoint of the edge, is the boundary line which belongs to both subdomains and , and is the space charge density at the grid point (Fig. 3.4).

The remaining task is to find an approximation for the projection of the dielectric flux density . This is done by the finite difference approximation

(3.21) | ||

(3.22) |

With eqn. (3.20) and eqn. (3.21), the discretization of POISSON's equation can be concluded.