  HTS are feasible for hight power applications because of the smaller
consumption demand of the cooling system in comparison to the whole power
device. Real industral devices contain superconductors with 2D and 3D geometry
(coated conductors tapes represent an example of 2D geometry, since the
superconducting layer is very thin). In order to know the feasibility and the
optimum design of a certain device, there is a need of software tools. These
Numerical tools have hight requirements like fast computation, a physical model
for any E(J) relation of the superconductor and any complex geometry such as
coils, motors and generators, where E is the electric field and J is the
current density. In this work we present a 3D variational model based on a
functional that restricts the problem in the superconductor volume. We show the
magnetization process of a thin film and a 3D bulk sample. We compare our model
of the thin film geometry with the thin film formula, reaching a good
agreement. We also compare a striated tape, where the filaments are connected
by linear material, with a FEM model. We present several results for a thin
film with constant critical current density, Jc, magnetic-field dependent Jc,
and an anisotropic E(J) relation. For the latter, E is not parallel to J when
the magnetic flux density is not perpendicular to J (force free situation). The
last studied situation is the 3D cubic sample. We find the time dependence of
the current density and AC loss for each situation. In the cubic bulk sample,
we found a non-negligible component of the current density in the direction of
the applied field. The presented numerical method is very promising for 3D
modeling of superconducting samples and power applications.
