On adaptive refinement for boundary integral methods in electrostatics

Numerical techniques based upon boundary integral methods like charge simulation or Galerkin boundary elements are still warmly received in the HV community because they are relatively easy to implement and use, and because they are accurate. However, the results can be sensitive to the quality of the discretization. In this work we introduce an efficient refinement scheme that automatically chooses the sections of conducting and dielectric boundaries where new nodes should be placed. The numerical results compare favorably to canonical solutions, and the method is shown to be effective on more complicated practical geometries.