Algebra of Fractal Vector as a Tool for Mapping Two Different Mashes

The breakdown voltage during interruption of capacitive currents is defined by two physical quantities: the electric field and the gas density field, which are calculated in different calculation domains and using different mashes. In order to calculate the breakdown voltage, it is necessary to map these two mashes and calculate the ratio density/electric field in every calculation point. The straightforward solution is to pair each density cell with the nearest cell from the electric field mesh, based on their coordinates. Although this solution gives good results, it is very time consuming. Therefore, this paper presents a new approach for mapping of two meshes based on the algebra of fractal vector, so called Bosnian algebra. This approach does not search the meshes for the closest pair based on the coordinates of each point, but instead uses only the assigned cell indexes and simple fractal operations to determine the neighboring cells. This way, the search for the nearest pair is much more efficient and faster.