Application of the finite elements method to the capacitance calculation

The most popular instrumentation used in the Electrical Engineering, presents edges that in the presence of an important electric field, act like as concentrating of electrostatic load and for they turn in the points with major probability of acting as way of an electrostatic discharge. The study from the electrostatic point of view of the behaviour of an edge, presents a singularity, since in this point the equations of continuity are not applicable. To calculate the existing load in these singularities, there have developed numerous studies and equations[1-5], which have given place to different iterative methods as the random walk [6-8], first-passage [9], last-passage [10], last-passage Monte Carlo [11;12], etc [6;13-15]. The problem is in that all these methods work for a few very studied geometries and stop doing it when the different geometry. This generates the need to use algorithms that allow to solve of generic form any type of geometry. The aim of this work is to calculate the capacitance of simple geometries by means of the finite elements method, with the but to see the influence of the edgeeffect in the entire capacitance. The first geometry to study is a unit cube of (length of edge is one meter), with that there is validated the mesh and the loop of calculation. The second geometry, is formed by two conducting parallel plates of length and thickness are a variable parameters. With this model one tries to justify the employment of the finite elements method to solve the proper singularities of this geometry.