  The time harmonic Maxwell equations are of current interest in computational
science and applied mathematics with many applications in modern physics. In
this work, we present parallel finite element solver for the time harmonic
Maxwell equations and compare different preconditioners. We show numerically
that standard preconditioners like incomplete LU and the additive Schwarz
method lead to slow convergence for iterative solvers like generalized minimal
residuals, especially for high wave numbers. Even more we show that also more
specialized methods like the Schur complement method also yield slow
convergence. As an example for a highly adapted solver for the time harmonic
Maxwell equations we use a combination of a block preconditioner and a domain
decomposition method (DDM), which also preforms well for high wave numbers.
Additionally we discuss briefly further approaches to solve high frequency
problems more efficiently. Our developments are done in the open-source finite
element library deal.II.

Numerical Analysis;Numerical Analysis