A two-level spectral preconditioning for the finite element method

An efficient auxiliary space preconditioning (ASP) was proposed for the linear matrix equation that was formed by the frequency-domain finite element method. A new two-level spectral preconditioning utilizing auxiliary space preconditioning is presented to solve the linear system. This technique is a combination of ASP and a low-rank update spectral preconditioning, in which the restarted deflated generalized minimal residual GMRES with the newly constructed spectral two-step preconditioning is considered as the iterative method for solving the system. Numerical experiments indicate that the proposed preconditioning is efficient and can significantly reduce the iteration number.