Implementation of some iterative matrix solvers in simulation of the wave propagation problem using the time-harmonic finite difference algorithm

In this paper, the formulation of two-dimensional finite difference frequency domain (FDFD) for heterogeneous and lossy materials is presented. But the main attention is focus on the efficient formulation of the matrix solver. Contemporary, the numerical models are consisted of a large-scale sparse complex matrix, therefore the specific formulation of the solver enable to improve the properties of the proposed algorithm. Two iterative subroutines for the complex equation are presented and validated, i.e. the BiConjugate Gradient Stabilized method (BiCGStab) and the Generalized Minimum Residual method with restarts (GMRES(m)). The stability and performance of these algorithms are tested using model based on typical building construction including concrete column.