The effect of magnetic fields in the Equations of State (EoS) of compact objects is the splitting of the pressure in two components, one parallel and the other perpendicular to the magnetic field. This anisotropy suggests the necessity of using structure equations considering the axial symmetry of the magnetized system. In this work, we consider an axially symmetric metric in spherical coordinates, the γ-metric, and construct a system of equations to describe the structure of spheroidal compact objects. In addition, we connect the geometrical parameter γ linked to the spheroid's radii, with the source of the anisotropy. So, the model relates the shape of the compact object to the physics that determines the properties of the composing matter. To illustrate how our structure equations work, we obtain the mass-radii solutions for magnetized White Dwarfs. Our results show that the main effect of the magnetic field anisotropy in White Dwarfs structure is to cause a deformation of these objects. Since this effect is only relevant at low densities, it does not affect the maximum values of magnetized White Dwarf's masses, which remain under Chandrasekhar limit. arXiv:1807.09943v3 [astro-ph.HE]

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In this work, the propagation of an ultrasonic pulse in a thin plate is computed solving the differential equations modeling this problem. To solve these equations finite differences are used to discretize the temporal variable, while spacial variables are discretized using Finite Element method. The variational formulation of the problem corresponding to a fixed value of time is obtained and the existence an uniqueness of the solution is proved. The proposed approach leads to a sequence of linear systems with the same sparse, symmetric and positive defined matrix. The free software FreeFem++ is used to compute the approximated solution using polynomial triangular elements. Numerical experiments show that velocities computed using the approximated displacements for different frequency values are in good correspondence with analytical dispersion curves for the phase velocity.