Computational relaxation method for modeling electrostatic systems with non-trivial geometries

Through electrostatic potential, it is possible to analyze an electromagnetic system and find the generated electric field and charge distribution for a given setup. However, most boundary conditions prove to be impossible to solve analytically. In the following paper, we present a computational relaxation method for modeling the potential, electric field and charge density of 2D electromagnetic systems with non-trivial geometries. By performing the experimental realization of finite parallel plates, we find an astonishing agreement between experimental results and our model. We study the uncertainties introduced by the model by comparing our results with theoretical predictions in the specific case of infinite parallel wires, and show that the error rate drops exponentially as the system size increases. Finally, the number of iterations required to reach equilibrium has also been analyzed for different lattice-sweeping methods. (paper)