Computation of eigenvectors in heterogeneous media as updates from homogenized estimates

Régis Cottereau (1) , David Colas (1) , Cédric Bellis (1) , Bruno Lombard (1)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

In this talk, we discuss the problem of computing eigenvalues and eigenvectors of a heterogeneous material or domain, and the numerical schemes to approximate them. We propose an improvement over the traditional Rayleigh quotient technique for the update of the eigenvalues, and discuss specifically the initialization of the iterative algorithm. We propose to use the homogenized equation to compute initial estimates and assess numerically the behavior of the algorithm when eigenmodes are actually localized.

Mots clés: Waves in heterogeneous media; Vibrations of heterogeneous materials; Eigenvalue analysis; Homogenization; Anderson Localization

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

Régis Cottereau, David Colas, Cédric Bellis, Bruno Lombard. Computation of eigenvectors in heterogeneous media as updates from homogenized estimates. 15ème colloque national en calcul des structures, Université Polytechnique Hauts-de-France [UPHF], May 2022, 83400 Hyères-les-Palmiers, France. ⟨hal-03717594⟩