Direct finite element solution for the capacitance, conductance or inductance, and force in linear electrostatic and magnetostatic problems

Abstract

Presents a direct solution method for the determination of quantities such as capacitance, conductance and inductance from the finite element representation of electrostatic and magnetostatic problems. The method can be used to complement existing finite element software which utilizes a field approach, or can be used for determining such quantities without the requirement for intermediate determination of a potential distribution within the system. Expresses the quantities in terms of parameters which depend only on the materials used in the system and their geometric distribution. In multi‐electrode systems, the direct method allows for the determination of the entire capacitance, inductance or conductance matrix in a single factorization process, without the need for the repeated numerical determination and evaluation of the potential distribution for each electrode in turn. The direct solutions for capacitance and inductance can be used to derive expressions for the forces and torques within the system, using the principle of virtual work.