A new hybrid model using electric field formulation for 3-D eddy current problems

Finite element modeling of the deformation of magnetoelastic film

“…The redundancy of the fields and arbitrariness of gauge conditions leads to a great variety of finite element formulations for electromagnetics. An example of anẼ-field formulation can be found in [12], in this formulation the electric field is the only variable. Examples of theH-field formulation can be found in [13,14], in this formulation the magnetic field is the only variable.…”

Modeling of photonic crystal optical fibers with finite elements

“…Therefore, we choose now an electric field formulation (dual to the magnetic one) to get simple boundary conditions because the tangential component of the electric field is null [8], what is not the case of the tangential magnetic field equal to the surface current.…”

“…The numerical formulation is given by the following residue [2], [3]: (8) where the unknown field is now a discrete Hilbert space, i.e., with a finite dimension equal to the number of numerical parameters to be determined. This formulation involves both a transverse field in the section of the guide and a longitudinal field along its axis.…”

A QR Accelerated Volume-to-Surface Boundary Condition for the Finite-Element Solution of Eddy-Current Problems

“…Various formulations for the eddy current equations exist and have been extensively reviewed and studied in the literature. These include formulations which solve for the electric field (the E field formulation) [1], [2], [3], the magnetic field (the H field formulation) [4], [5] or for the potential field (the A-φ potential formulation) [6], [7], [8], [9]. Each formulation has its advantages and disadvantages for problems in computational electromagnetics.…”

“…The difficulty with this is twofold; one is the large number of unknowns and the second is matrix ill-conditioning. More sophisticated approaches include forming a magnetostatic problem in the nonconducing region using either the vector or scalar magnetic potential and coupling the two finite element solutions [6] [12], or employing a surface integral equation to correctly model the global boundary condition [1] [2] [13].…”