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Propose post processing methods for the edge finite element (FE) method on a tetrahedral mesh. They make it possible to deduce vector values on the vertices from scalar values defined on the edges of the tetrahedra.

The new proposed techniques are based on a least squares formulation leading to a sparse matrix system to be solved. They are compared in terms of accuracy and CPU time on a FEs formulation for open boundary – frequency domain problems.

A significant improvement of vector values accuracy on the vertices of the tetrahedra is obtained compared to a classical approach with a very small additional computation time.

This work presents techniques: to obtain the values at the initial nodes of the mesh and not inside the tetrahedra; and to take into account the discontinuity to the interface between two media of different electromagnetic properties.

The purpose of this paper is to introduce a novel methodology for uncertainty quantification in large-scale systems. It is a non-intrusive approach based on the unscented transform (UT) but it requires far less simulations from a EM solver for certain models.

The methodology of uncertainty propagation is carried out adaptively instead of considering all input variables. First, a ranking of input variables is determined and after a classical UT is applied successively considering each time one more input variable. The convergence is reached once the most important variables were considered.

The adaptive UT can be an efficient alternative of uncertainty propagation for large dimensional systems.

The classical UT is unfeasible for large-scale systems. This paper presents one new possibility to use this stochastic collocation method for systems with large number of input dimensions.