Comparison of quasi minimal residual and bi-conjugate gradient iterative methods to solve complex symmetric systems arising from time-harmonic magnetic simulations

Finite element discretizations of low-frequency, time-harmonic magnetic problems lead to sparse, complex symmetric systems of linear equations. The question arises which Krylov subspace methods are appropriate to solve such systems. The quasi minimal residual method combines a constant amount of work and storage per iteration step with a smooth convergence history These advantages are obtained by building a quasi minimal residual approach on top of a Lanczos process to construct the search space. Solving the complex systems by transforming them to equivalent real ones of double dimension has to be avoided as such real systems have spectra that are less favourable for the convergence of Krylov-based methods. Numerical experiments are performed on electromagnetic engineering problems to compare the quasi minimal residual method to the bi-conjugate gradient method and the generalized minimal residual method.