  We focus on non-stationary Maxwell equations defined on a regular patch of
elements as considered in the isogeometric analysis (IGA). We apply the
time-integration scheme following the ideas developed by the finite difference
community [M. Hochbruck, T. Jahnke, R. Schnaubelt, Convergence of an ADI
splitting for Maxwell's equations, Numerishe Mathematik, 2015] to derive a weak
formulation resulting in discretization with Kronecker product matrices. We
take the tensor product structure of the computational patch of elements from
the IGA framework as an advantage, allowing for linear computational cost
factorization in every time step. We design our solver to target simulations of
electromagnetic waves propagations in non-regular biological tissues. We show
that the linear cost of the alternating direction solver is preserved when we
arbitrarily vary material data coefficients across the computational domain. We
verify the solver using the manufactured solution and the problem of
propagation of electromagnetic waves on the human head.
