A new splitting preconditioner for the iterative solution of complex symmetric indefinite linear systems

In this paper, we consider preconditioned simplified Hermitian normal splitting (PSHNS) iteration method for solving complex symmetric indefinite linear systems, analyze the convergence of the PSHNS iteration method and discuss the spectral properties of the PSHNS preconditioned matrix. Using discrete Sine transform (DST), we apply a fast algorithm to solve the subsystem during the preconditioning process. Numerical experiments arising from the Helmholtz equation show the effectiveness and robustness of the PSHNS preconditioner. In addition, the GMRES method with the PSHNS preconditioner demonstrates meshsize-independent and wavenumber-insensitive convergence behavior.