Finite element computation of Green's functions

Denis Duhamel (1)

1 LAMI - Laboratoire d'Analyse des Matériaux et Identification

Green's functions are important mathematical tools in mechanics and in other parts of physics. For instance, the boundary element method needs to know the Green's function of the problem to compute its numerical solution. However, Green's functions are only known in a limited number of cases, often under the form of complex analytical expressions. In this article, a new method is proposed to calculate Green's functions for any linear homogeneous medium from a simple finite element model. The method relies on the theory of wave propagation in periodic media and requires the knowledge of the finite element dynamic stiffness matrix of only one period. Several examples are given to check the accuracy and the efficiency of the proposed numerical Green's function.

Mots clés: Green's function; periodic structure; wave; waveguide; finite element; dynamic

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Denis Duhamel. Finite element computation of Green's functions. Engineering Analysis with Boundary Elements, 2007, à paraitre. ⟨10.1016/j.enganabound.2007.04.002⟩. ⟨hal-00150429⟩