  We focus on non-stationary Maxwell equations defined on a regular patch of
elements as considered in the isogeometric analysis. 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
formulations resulting in a discretization with Kronecker product matrices.
Going further, we investigate the application of the residual minimization (RM)
method for stabilization of the Maxwell equations within the isogeometric
analysis setup. The residual minimization method is introduced in every time
step of the implicit time integration scheme. We introduce the RM in such a way
that we preserve the Kronecker product structure of the matrix. We take the
tensor product structure of the computational patch of elements from IGA
framework as an advantage, allowing for linear computational cost factorization
in every time step, with the automatic stabilization guaranteed by the RM
method.
