An innovative approach has been recently proposed for the voltage breakdown prediction in high-voltage systems, insulated by large vacuum gaps. This approach is based on complementary geometric formulations for electrostatics coupled to the analytical solution of the equations of motion for charged particles. In this paper, a goal-oriented local mesh refinement technique is introduced, which allows to increase the rate of convergence of the solution, enabling an effective voltage breakdown prediction also in large-scale systems with complex geometries.