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We focus on non-stationary Maxwell equations defined on a regular patch ofelements as considered in the isogeometric analysis (IGA). We apply thetime-integration scheme following the ideas developed by the finite differencecommunity [M. Hochbruck, T. Jahnke, R. Schnaubelt, Convergence of an ADIsplitting for Maxwell's equations, Numerishe Mathematik, 2015] to derive a weakformulation resulting in discretization with Kronecker product matrices. Wetake the tensor product structure of the computational patch of elements fromthe IGA framework as an advantage, allowing for linear computational costfactorization in every time step. We design our solver to target simulations ofelectromagnetic waves propagations in non-regular biological tissues. We showthat the linear cost of the alternating direction solver is preserved when wearbitrarily vary material data coefficients across the computational domain. Weverify the solver using the manufactured solution and the problem ofpropagation of electromagnetic waves on the human head.

Alternating directions implicit higher-order finite element method for  simulations of time-dependent electromagnetic wave propagation in non-regular  biological tissues