Charge Simulation Method (CSM)

Charge Simulation Method :

• This method is introduced by kelvin in 1872.
• H. Steinbingler developed this method for digital computation of electric fields in this dissertation submitted to the technical university Munich in 1969.
• The charge simulation methods is an integral equation technique unlike Finite Element Method (FEM) which is based on differential technique.
• It makes use of mathematical linearity and expressed Laplaces equation as a summation of particular solution due to set of known discrete fictitious charges.
• In effect the actual E-field due to the charges present on the electrode and dielectric boundaries is simulated by the field formed by a number of fictitious charges, which are placed outside the region where the field solution is desired.
• Location of the fictitious charges are predetermined by the programmer, while the magnitudes of these charges are found by satisfying the boundary condition at the selected number of contour points on the boundaries.
• The unknown charges are computed from the equation

                                                                       ...(1)

          where, [P] is the potential coefficient matrix

                      [Q] is the column vector of unknown charges

          and      [V] is the potential of the contour points (Boundary conditions)

• On knowing these  charges the potential and electric field intensity at any point can be determined from the combined effect of these charges.
• These are two variations of this method :

1. CSM with descrete charges
2. CSM with area charges

• CSM with discrete charges is based on the principle that the real surface charges on the surface of electrodes or dielectic interfaces are replaced by a system of point and line charges located outside the field domain.
• The position and the type of simulation charges are to be determined first and then the magnitudes of the charges are calculated so that their combined effect satisfies the boundary conditions.
• After determining these magnitudes by using the method of solving a system of linear equations, it is to be verified whether the systems of simulation charges fulfills the boundary  conditions between the location points with sufficient accuracy.
• Then the voltage and field strength at any point within the field domain can be calculated analytically by the superposition of simple potential and gradient functions.