The numerical simulation of the equilibrium of the plasma in a tokamak as well as its self-consistent coupling with resistive diusion should benet from higher regularity of the approximation of the magnetic ux map. In this work, we propose a nite element approach on a triangular mesh of the poloidal section, that couples piece-wise linear nite elements in a region that does not contain the plasma and reduced Hsieh-Clough-Tocher nite elements elsewhere. This approach gives the exibility to achieve easily and at low cost higher order regularity for the approximation of the ux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details in the rest of the computational domain. The continuity of the numerical solution at the coupling interface is weakly enforced by mortar projection. A new technique for the computation of the geometrical coecients is also presented.

This paper studies the effects of a microwave excitation on the transverse vibrations of viscoelastic bars placed inside unconventional electromagnetic waveguides. Its purpose is to present a general approach that can be applied to analyze and to interpret the physical phenomena risen during the heating process. These phenomena were not predicted either by conventional experiments or by existing theoretical models. To measure the bar transverse deformations, an opening line and a hole have been made respectively on one of the small transverse sides of the waveguides. The comparison between the spectra of the experimental transverse velocities measured with these two waveguides has pointed out some differences. Theoretical and finite element (FE) simulations of the experiments have been firstly applied to figure out the nature of these variations. The analysis is conducted by a parameterized approach that takes into account the effects of the opening line made along the waveguide on both the propagation of the electromagnetic power density and the temperature rise distribution inside the sample. Good agreements between the models and the experimental data are demonstrated. Furthermore, the method has also shown a sudden asymmetric temperature distribution that leads to the generation of new flexural modes. These last modes are specific to the experiment used to apply the microwave induce acoustic technique.