A FEM/BEM for axisymmetric electromagnetic and thermal modelling of induction furnaces

Abstract

Secondly, it is necessary to give a precise mathematical definition of the termappearing in Equation (19), because it does not make sense for any G ∈ Y. To attain this goal, for k = 1, . . . , m, let us denote by k the solution in H 1 ( k \ k ), unique up to a constant, of the following problem:). Since the current density J = E satisfies div J = 0 in and J · n = 0 on , we havewhere k denotes the boundary of k . Note that, while the right-hand side of the previous equality does not make sense for any G in Y, the left-hand side does.

FEM-BEM coupling methods for Tokamak plasma axisymmetric free-boundary equilibrium computations in unbounded domains

“…The numerical solution on the interior domain is coupled through boundary conditions to the Green's function representation of the solution in the unbounded exterior domain. This approach is used in many other application areas such as electromagnetics [22,41,4] or elasticity [12,5,37] and falls in the framework of boundary integral equations. The boundary integral equations enable to reduce problems on unbounded domains to problems on boundaries which can then be coupled to any numerical method for the interior bounded domain.…”

Voltage and Current Excitation for Time-Harmonic Eddy-Current Problems

“…Far from being complete, let us only mention the contributions in [11], [19], [17], [18], [25], [26], [23], [16], [10], [20], [8], [6] and the references therein.…”

“…A similar formulation has been proposed in [20], [6] (in the former paper, replacing the source V ρ C by V grad Φ C , Φ C being a function jumping by 1 through a section Σ of Ω C ). However, in these papers the electric field is not the solution E C to (18) 1 , but it is corrected in Ω C by adding the source term.…”

“…In [8] a formulation for the electric port case with assigned current intensity is given, leading to the solution also obtained in [5] for Case C; however, for Case A it can be checked that the Faraday law is violated on the cutting surface Ξ (instead, the violation of the Faraday law across the interface Γ occurs in [6], where the internal conductor case is considered).…”

“…In this paper we have proved existence and uniqueness of the solution for the infinite dimensional case, but a complete analysis of a finite element approximation method could be a more delicate point. However, this approach has been used in [6] for an axisymmetric problem, with good numerical performances.…”