Efficient finite element modeling for 3D eddy currents in GO silicon
steel laminations

Weiying Zheng
Academy of Mathematics and Systems Science
State Key Laboratory of Scientific and Engineering Computing
Chinese Academy of Sciences

Grain-oriented (GO) silicon steel laminations are widely used in iron
cores and shielding structures of large power transformers. The
lamination stack consists of many sheets which are very thin and
coated with an insulating film of 3-5 microns thickness. The ratio of
the largest scale to the smallest scale of the system is usually
10^6. Accurate simulations for 3D eddy currents in GO silicon steel
laminations usually necessitate very anisotropic or very large number
of elements. Since the magnetic permeability is nonlinear and
anisotropic, the discrete problem is very ill-conditioned and direct
computations of 3D eddy currents are usually unrealistic. In this
talk, I first propose a new eddy current model which removes the
coating film from the system and thus reduces the scale ratio from 10^6
to 10^3. Then I will talk about the wellposedness of the new model
briefly. A conforming finite element approximation will be presented
by coupling edge element methods and nodal element methods. At last, I
will present the numerical experiments for an engineering benchmark
problem --- Team Workshop Problem 21c by parallel computations on
unstructured tetrahedral meshes.