Accelerating the charge inversion algorithm with hierarchical matrices for gas insulated systems

Surface charges accumulating on dielectrics during long-time operation of Gas Insulated High Voltage Direct Current (HVDC-GIS) equipments may affect the stable operation and could possibly trigger surface flashovers. In industrial applications, to quantify and identify the location of the surface charge accumulation from experimental measurements, the surface potential distribution is evaluated using, e.g., electrostatic probes, then the charge density is determined by solving an electrostatic problem based on an inversion procedure known as Charge Inversion Algorithm. The major practical limitation of such procedure is the inversion and the storage of the fully dense matrix arising from the representation via Integral Equations of the electrostatic phenomenon, resulting in O(N 3) computational complexity and O(N 2) memory requirement. In this paper it is shown how hierarchical matrices can be efficiently used to accelerate the charge inversion algorithm and, more importantly, reduce the overall memory requirement.