Before revision:  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 .
After revision:  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 . 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 .