  A method of numerically solving the Maxwell equations is considered for
modeling harmonic electromagnetic fields. The vector finite element method
makes it possible to obtain a physically consistent discretization of the
differential equations. However, solving large systems of linear algebraic
equations with indefinite ill-conditioned matrices is a challenge. The high
order of the matrices limits the capabilities of the Gaussian method to solve
such systems, since this requires large RAM and much calculation. To reduce
these requirements, an iterative preconditioned algorithm based on integral
Laguerre transform in time is used. This approach allows using multigrid
algorithms and, as a result, needs less RAM compared to the direct methods of
solving systems of linear algebraic equations.
