A BETL application for electrostatic simulations

This is a very simple example of an electrostatic simulation. The according boundary value problem corresponds to an outer Dirichlet problem for the Laplace equation. The Model depicts an electric device which consists of six electrodes surrounded by a grounding box. The grounding box as well as five electrodes feature a zero voltage. The remaining Electrode contains a fixed voltage unequal to zero. The left model within the table below shows the initial setup. There, the electrode carrying the non-zero voltage is marked in red while all grounded parts are coloured in blue.

Note that the voltage is nothing but a potential by what it can be identified as the Dirichlet datum. The visualisation on the right hand side shows the computed Neumann data on the surface. From a physical point of view the Neumann data correspond to the electric field strength. The electric field strength is important to know since in the end it determines the design of the electric device.

prescribed voltage calculated electric field strength