This paper presents a new numerical model for computing the current density, field
distributions and AC losses in superconductors. The model, based on the direct magnetic field
H
formulation without the use of vector and scalar potentials (which are used in
conventional formulations), relies on first-order edge finite elements. These elements are
by construction curl conforming and therefore suitable to satisfy the continuity
of the tangential component of magnetic field across adjacent elements, with
no need for explicitly imposing the condition . This allows the overcoming of one of the major problems of standard nodal elements with
potential formulation: in the case of strong discontinuities or nonlinearities of the
physical properties of the materials and/or in presence of sharp corners in the
conductors’ geometry, the discontinuities of the potentials’ derivatives are unnatural
and without smoothing artifices the convergence of the algorithm is put at risk.
In this work we present in detail the model for two-dimensional geometries and we test it
by comparing the numerical results with the predictions of analytical solutions for simple
geometries. We use it successively for investigating cases of practical interest involving
more complex configurations, where the interaction between adjacent tapes is
important. In particular we discuss the results of AC losses in superconducting
windings.