The presented systems with magnetically coupled windings are solved with
the finite element method. If the issue of voltage supply is analyzed, a system of linear
equations with a partially skew-symmetric sparse matrix is obtained. Iterative methods
used to solve a system of equations are particularly effective for symmetric matrices. Resultant
equations can be reduced to this symmetrical form by using the method known
from the literature [1]. The ratio of the maximum to the minimum eigenvalue of the main
matrix of this circuit, which is the condition number, is however very high. This means
that the problem is ill-conditioned and leads to a very long iterative solution process. The
method presented in the article allows for a direct solution of a system of equations on its
part, corresponding to high eigenvalues of the system matrix. The remaining part of the
system of equations is solved by iterative methods. This part has much better condition
number, and therefore the computational process is fast. The proposed iterative process
depends on multiplication of a sparse matrix by vectors. It is not necessary (and possible)
to store the entire matrix. This is especially important for larger sizes of a matrix.
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