Conventional Surface Charge Methods

The Surface Charge Method divides the surface of a body into a number of planar elements and solves for the individual charges of the elements by assigning variables to them.

＜Calculation method (for electrodes)＞
(1) Suppose there are multiple electrodes.
(2) The potential created by the charge of each electrode can be calculated by Coulomb's law.
(3) Conversely, if the potential of each electrode is specified, the charges of the electrodes can be calculated by solving simultaneous equations with the charges of the electrodes as unknowns.
(4) Once the charges of the electrodes are known, the potential and electric field at any location can be calculated.

Calculation of the electric field of electrodes using the "Surface Charge Method".
(calculation time less than 1 second)
Eight electrodes were given positive and negative potentials to calculate the charge density and spatial electric field.

Improvements by ELF

However, the " Surface Charge Method" has no variables that represent polarization inside the dielectric.
Therefore, it does not take into account the effect that polarization is sent to neighboring elements by canceling polarization charges between neighboring elements,
which causes cases where elongated dielectrics cannot be calculated correctly.

On the left is the " Surface Charge Method" and on the right is the " ELF's original integral element method" (polarized charge elements).

There are two ring-shaped dielectrics with a relative permittivity of 20, and red and green linear (flat) electrodes on the top and bottom.
The electrodes were given positive and negative potentials to apply electric fields to the dielectrics.

In the " Surface Charge Method," there are no polarization vectors inside the elements, so the electric flux does not pass through the interior of the dielectric, and are immediately emitted into space.
ELF's method solves the problem correctly.

To conventional Magnetic Moment Method ≫

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