Hybrid A-EHS Method for Fast Computation in Superconducting Bulks

In this article, a two-dimensional hybrid finite-element formulation is proposed to further reduce the computational time required for the time simulation of superconducting (SC) bulks. Low computational time formulations are important for the design stage of electrical machines with superconductors, where optimization tools are typically used. The proposed hybrid formulation is based on the partitioned
E
-
H
electromagnetic scheme (
EHS
) formulation and the magnetic vector potential formulation (
A
-formulation). The
EHS
formulation is used to solve the domains with highly nonlinear electric materials, while the
A
-formulation is used to solve the nonelectric domains. The main characteristics of the
EHS
are its partitioned formulation, where the matrix form of Ampère's and Faraday's laws is separated and computed
a priori
, and the electric resistivity is defined at each node. The
EHS
formulation is first compared with the
H
-formulation for a single SC domain and then integrated with an
A
-formulation and compared with the
H
and
H
-
φ
formulations to simulate a bulk surrounded by air. Results verify the excellent accuracy of the
EHS
and
A-EHS
formulations, and a promising reduction of computational time is observed, with more emphasis on low levels of magnetization of the SC sample. When compared with the
H
-
φ
formulation, a time reduction between 48% (6 T) and 90% (1 T) is obtained.