We present an open finite element framework, called GetDDM, for testing optimized Schwarz domain decomposition techniques for time-harmonic wave problems. After a review of Schwarz domain decomposition methods and associated transmission conditions, we discuss the implementation, based on the open source software GetDP and Gmsh. The solver, along with ready-to-use examples for Helmholtz and Maxwell's equations, is freely available online for further testing.

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The 5 D terms of Fe 2+ and Cr 2+ in the tetrahedral potential at cation sites in II-VI compounds split into orbital doublet and triplet states. While in Cr 2+ the orbital triplet has lower energy than the doublet, the opposite is the case in Fe 2+ . Both ions have singlet ground states after the spin-orbit interaction is taken into account and, hence, both are Van Vleck paramagnets. The optical absorption spectra of Fe and Cr based materials differ and are explained on the basis of a dynamic Jahn-Teller effect in the former and a static one in the latter. These considerations permit us to explain the optical as well as the magnetic properties observed in these materials.

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A theoretical study of the isotopic-mass dependence of the internal transitions of Fe 2+ at a cation site in a cubic zinc-blende semiconductor is presented. The model used is based on crystal-field theory and includes the spinorbit interaction and a weak dynamic Jahn-Teller coupling between the 5 Γ 5 excited manifold of Fe 2+ and a local vibrational mode (LVM) of Γ 5 symmetry. The mass dependence of the LVM frequency is described, in the harmonic approximation, within two different limits: the rigid-cage model and a molecular model. In the rigidcage model, the Fe 2+ ion undergoes a displacement but the rest of the lattice is fixed. In this case, a simple M -1l2 dependence of the frequency is obtained and the Jahn-Teller energy, E JT is independent of the mass. In the molecular model, the four nearest neighbors of the magnetic ion are allowed to move and the LVM then behaves as the Γ 5 mode of a MX 4 tetrahedral molecule leading to a more complicated dependence of the frequency on the isotopic mass and to a mass-dependence of E JT . The theoretical results obtained with these two models are compared with the observed isotopic shifts of the zero-phonon lines in InP:Fe and GaP:Fe corresponding to an optical transition between the vibronic Γ 1 ground state and the lowest Γ 5 state originating from the 5 Γ 5 excited orbital multiplet. A prediction of the isotopic shifts of the zero-phonon line in GaAs:Fe is also presented.