Education

    February 1995

Degree in Mathematics at the University of Milano (Italy)
obtained with the highest score

    Approximation of elastostatic and elastodynamic problems with the finite element method
    Thesis Advisor : Prof. Alfio Quarteroni


October 1997 - Mai 2000

PhD in Numerical Analysis at Paris VI University (France) obtained with the highest score
Summary

The work presented in this Thesis concerns the mathematical study and the implementation of a numerical method to simulate the distribution of Foucault's currents in moving electromagnetic devices. The starting point of this study is the system of Maxwell's equations and their formulation for magnetodynamic problems. Within the domain decomposition framework, adapted to deal with geometries composed of a fixed and a moving part, we propose a (spatial) non-conforming discretization technique based on the mortar element method coupled with finite elements belonging to the Whitney's complex. This method allows to deal easily with meshes that do not match at the interface between the fixed and the moving part. The movement speed and the spatial discretization parameters are independent one of the others. The transmission conditions, to restore the continuity of the fields (or of one of their components) across the sliding interface, are weakly imposed by means of a suitable space of Lagrange multipliers. The discretization in time is done in a classical way by applying an implicit finite difference scheme. The final algebraic system has a symmetric, positive definite and well-conditioned matrix and is solved by the Conjugate Gradient procedure. The method analysed in this Thesis, has been successfully applied to solve the following problems: a scalar magnetodynamic problem in two dimensions, coupled and uncoupled with its mechanical aspect; a vector magnetodynamic problem in two dimensions; a vector magnetostatic problem in three dimensions. We have also proposed a first preconditioned algorithm of FETI type for the parallel solution of the two-dimensional vector magnetodynamic problem.


June 2008

HdR in Numerical Analysis at the Université de Nice Sophia-Antipolis (France)