The Robin Hood method  a novel numerical method for electrostatic problems based on a nonlocal charge transfer
Abstract
We introduce a novel numerical method, named the Robin Hood method, of solving electrostatic problems. The approach of the method is closest to the boundary element methods, although significant conceptual differences exist with respect to this class of methods. The method achieves equipotentiality of conducting surfaces by iterative nonlocal charge transfer. For each of the conducting surfaces nonlocal charge transfers are performed between surface elements which differ the most from the targeted equipotentiality of the surface. The method is tested against analytical solutions and its wide range of application is demonstrated. The method has appealing technical characteristics. For the problem with N surface elements, the computational complexity of the method essentially scales with N^alpha, where alpha < 2, the required computer memory scales with N, while the error of the potential decreases exponentially with the number of iterations for many orders of magnitude of the error, without the presence of the Critical Slowing Down. The Robin Hood method has a large potential of application in other classical as well as quantum problems. Some possible applications outside electrostatics are outlined.
 Publication:

arXiv eprints
 Pub Date:
 November 2004
 arXiv:
 arXiv:physics/0411192
 Bibcode:
 2004physics..11192L
 Keywords:

 Physics  Computational Physics;
 Physics  Classical Physics
 EPrint:
 26 pages, 12 figures