Comparison study of finite element methods to deal with floating conductors in electric field

In transient magnetic field computation, it is highly desirable if the stray capacitances among all conductors can be computed and their effects addressed conveniently. Because of the existence of floating conductors, the general finite element (FE) solver of Poisson's equation, which is a commonly used magnetic field solver, cannot be used to extract the capacitance matrix directly. In this paper, methods to deal with floating conductors in the electrostatic field for field solution, and capacitance matrix extraction using finite element method (FEM) are compared; their merits and shortcomings are discussed. A method to compute the electric field and extract the capacitance matrix to include the effect of floating conductors inside the solution domain is put forward. The merit of the proposed algorithm is that the general FE solver can be used without the need for any special program modification. A FE formulation to automatically include the capacitances in transient magnetic field is presented. By using the proposed method, users only need to input the information as how the conductors are connected. All the stray capacitances among conductors are automatically included in the solution of transient magnetic field with the proposed algorithm.