  Extensive research papers of three-dimensional computational techniques are
widely used for the investigation of human brain pathophysiology. Eddy current
analyzing could provide an indication of conductivity change within a
biological body. A significant obstacle to current trend analyses is the
development of a numerically stable and efficiency-finite element scheme that
performs well at low frequency and does not require a large number of degrees
of freedom. Here, a custom finite element method (FEM) solver based on edge
elements is proposed using the weakly coupled theory, which separates the
solution into two steps. First, the background field (the magnetic vector
potential on each edge) is calculated and stored. Then, the electric scalar
potential on each node is obtained by FEM based on Galerkin formulations.
Consequently, the electric field and eddy current distribution in the object
can be obtained. This solver is more efficient than typical commercial solvers
since it reduces the vector eddy current equation to a scalar one, and reduces
the meshing domain to just the eddy current region. It can therefore tackle
complex eddy current calculations for models with much larger numbers of
elements, such as those encountered in eddy current computation in biological
tissues. An example is presented with a realistic human brain mesh of 2 million
elements. In addition, with this solver, the equivalent magnetic field induced
from the excitation coil is applied, and therefore there is no need to mesh the
excitation coil. In combination, these significantly increase the efficiency of
the solver.
