École Nationale Supérieure de
Techniques Avancées

Abstract

In this thesis, time-harmonic Maxwell's equations are our main interest, in order to compute accurately the radar cross section of electromagnetic targets. To have a good precision in largescale experiments, higher-order finite element methods are used. In the scalar case, hexahedral spectral finite element, with mass lumping, provide a fast matrix-vector product with a low storage. In the vectorial case, Nedelec's first family hexahedral element doesn't lead to mass lumping, but a fast matrix-vector can be found. Numerical results in 3-D show the efficiency of this algorithm. The case, where the geometry is invariant under rotation, is treated. This symmetry leads to solve a sequence of 2-D independent problems. A higher-order finite element method is proposed. This method is coupled with higher-order boundary element method.