An Iterative Finite Element Perturbation Method for Computing Electrostatic Field Distortions

A finite element perturbation method is developed for computing electrostatic field distortions and the ensuing charges and forces on moving conductive regions subjected to fixed potentials. It is based on the subsequent solution of an unperturbed problem in a complete domain, where conductive regions have been extracted, and of perturbation problems in subdomains restricted to the surroundings of the added conductive regions. The solution of the unperturbed problem serves as source (with a very reduced support) for the perturbation subproblems. For every new position of the conductors, the solution of the unperturbed problem does not vary and is thus reused; only the perturbation subproblems have to be solved. Further, this approach allows for the use of independent and well-adapted meshes. An iterative procedure is required if the conductive regions are close to the sources.