Performance of the Alternating Direction Implicit Scheme With Recursive Sparsification for the Finite Element Time Domain Method

In this paper, we solve the ε and B mixed finite element time domain formulation using the alternating-direction implicit (ADI) scheme in time. To save computational cost, the algorithm is improved using a recursive sparsification procedure that approximates the inverse matrix needed to calculate the electric field. Although the method is unconditionally stable, we show that the numerical performance of the algorithm is strongly related to the time step. Numerical results demonstrated that for the same accuracy our approach is much faster than the ADI with Cholesky factorization.