The Robin Hood method—A new view on differential equations

A novel, efficient and numerically cheap approach to problems in electrostatics is presented. The core principle of this approach, named the Robin Hood (RH) method, is achieving equipotentiality of the conducting surfaces by the iterative nonlocal charge transfer. At the fundamental level the RH method is significantly different approach from the current more standard approaches in boundary element methods or various approaches in finite difference methods the most prominent one being relaxation technique with multigrid implementation. The important elements of the implementation of the method, together with the relevant details, are described. The efficiency of the method is exemplified in a number of nontrivial and realistic configurations. The attractive technical characteristics of the RH method, such as linear scaling of the required computer memory with the number of elements, the geometrical convergence and absence of the critical slowing down, as well as the efficient parallelisation, are demonstrated. As an example of the overall performance of the RH method, the capacitance of the metal cube is calculated with the greatest accuracy up to date. A possible extension of the method to other problems beyond electrostatics is outlined.