The charge-density method of solving electrostatic field: Program and error analysis

The Charge-Density method of solving electrostatic field has many advantages over the finite difference or finite element method, but its accuracy and fitness are still in question. By direct evaluating electrical potentials, the errors along surface of the electrode are plotted, which are the maximum errors for an electrostatic problem. It is shown that higher accuracy will be reached if more sub-regions are chosen at where the charge density is high or at the region near the area where the field is to be calculated. This will be helpful to understand and use the method efficiently. It is more convenient and accurate to use the chargedensity method when we deal with the calculation of an electrostatic system having a great difference in size between electrodes (such as the point emitter diode). Using the information of error on the surface of electrode, we can estimate the potential errors in each calculation or rearrange the sub-regions to improve the accuracy of the next calculation. A program is set up. The difference between the calculated data and that of E. Harting and F. H. Read (1976) is less than 1%.