Hybrid Domain Decomposition Solvers for the Helmholtz and the Time Harmonic Maxwell’s Equation

We present hybrid finite element methods for the Helmholtz equation and the time harmonic Maxwell equations, which allow us to reduce the unknowns to degrees of freedom supported only on the element facets and to use efficient iterative solvers for the resulting system of equations. For solving this system, additive and multiplicative Schwarz preconditioners with local smoothers and a domain decomposition preconditioner with an exact subdomain solver are presented. Good convergence properties of these preconditioners are shown by numerical experiments.