Electric circuit element boundary conditions in the finite element method for full-wave passive electromagnetic devices

Abstract

A natural coupling of a circuit with an electromagnetic device is possible if special boundary conditions, called Electric Circuit Element (ECE), are used for the electromagnetic field formulation. This contribution shows how these ECE boundary conditions can be implemented into the 3D-finite element method for solving coupled full-wave electromagnetic (EM) field-circuit problems in the frequency domain. The frequency response allows the extraction of a reduced order model of the analyzed device, accounting for all the EM field effects. The implementation is based on a weak formulation that uses the electric field strength E strictly inside the domain and a scalar potential V defined solely at the boundary. Edge elements for E are used inside the three-dimensional domain and nodal elements for V are used on its two-dimensional boundary. The weak formulation is described and implemented in the free environment Open Numerical Engineering LABoratory (onelab). The validation is carried out on 3D examples.

Dual Full-Wave Formulations with Radiant Electric Circuit Element Boundary Conditions. Application to Monopole Antenna Modeling

“…This work is an extension of our previous results referring to duality published for electrostatics (ES) and magnetic stationary field (MS) Ioan et al (2004Ioan et al ( , 2006b, and referring to the recent use of ECE boundary conditions for FW Ciuprina et al (2021Ciuprina et al ( , 2022Ciuprina et al ( , 2023, implemented in onelab, a software package that includes the mesh generator gmsh Geuzaine and Remacle (2009), and the finite element method (FEM) solver getdp Dular and Geuzaine.…”

“…in Dular et al (2000); Ren and Qu (2010) and their references. The present paper is a follow up of Ciuprina et al (2023) in which E and H FW FEM implementations for ECE BC without radiant parts on the boundary were validated against the analytic solutions for a cylindrical conductor and a coaxial cable. The novelty here is the addition of the radiant part at the boundary.…”

“…For the FW EM field regime, a sound and general theory for weak E-based and H-based formulations with electric and magnetic ports, for multiply connected domains and linear materials can be found in Hiptmair and Ostrowski (2021). In Ciuprina et al (2022) we showed how the E-based formulation, with an electric field strictly inside the domain and electric scalar potential on the boundary, can be implemented and used for parameter extraction. In Ciuprina et al (2023) the Hbased formulation (with a magnetic field inside the domain) was discussed and used for standard ECE, without a radiant surface.…”

“…In Ciuprina et al (2022) we showed how the E-based formulation, with an electric field strictly inside the domain and electric scalar potential on the boundary, can be implemented and used for parameter extraction. In Ciuprina et al (2023) the Hbased formulation (with a magnetic field inside the domain) was discussed and used for standard ECE, without a radiant surface. We consider the H formulation proposed in Ciuprina et al (2023) is different from the one in Hiptmair and Ostrowski (2021) because in our formulation the time domain correspondent involves convolution integrals and the scalar potential is defined only on the boundary.…”

“…In Ciuprina et al (2023) the Hbased formulation (with a magnetic field inside the domain) was discussed and used for standard ECE, without a radiant surface. We consider the H formulation proposed in Ciuprina et al (2023) is different from the one in Hiptmair and Ostrowski (2021) because in our formulation the time domain correspondent involves convolution integrals and the scalar potential is defined only on the boundary. Moreover, in our approach the topological analysis of the boundary is necessary, to find the cuts that make the magnetic scalar potential univalent, which is not needed in the E formulation.…”