Figure 2-4. The 7-Point Formulation of Laplace´s Equation
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For the calculation of electric and magnetic potential distribution inside the shielded box, the Laplace´s differential equation is solved. A 7-point formulation is derived from Laplace´s difference equation using the corresponding boundary conditions. The possible boundaries are: electric walls, magnetic walls and dielectric boundary. The 7-point formulation expresses the electrical potential at any grid point P inside the box as a function of potentials at 6 neighboring points and their distances to the point P (Figure 2-4).
For the numerical determination of the potential distribution inside the box, the iterative method of “Over Relaxation” (OR) is used. At first, an initial potential is assumed in all points. The potential at any point of grid is then corrected using the mentioned 7-point formulation. This procedure is repeated as long as the mean error between the corrected potential and the previously calculated potential for all points of grid is less than a defined iteration error. Using the potential difference between two points in x, y or z-direction, the electric and magnetic field distribution can be determined for all points inside the box.
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