Computation of 3D electrostatic local fields and forces using complementarity of dual formulations. Application for capacitance and torque calculations in micromotors

Recent studies in electromagnetic field computation show an interest of using dual formulations. They provide complementary energy bounds, which permits one to obtain global parameters such as impedance with minimum computation costs. The calculation of electromagnetic field by dual formulations ensures the use of Maxwell equations where the numerical errors are on the constitutive laws describing physical properties, this leads to an efficient indicator to auto-adaptive mesh refinement. The proposal in this article is to use two dual finite element formulations for calculating the 3D electrostatic field and to apply the virtual work principle for obtaining the local force distribution. In the analysis the Whitney elements are employed to ensure the physical continuity of working variables. An example of application of such analysis, the modelling of a variable capacitance micromotor, is presented.