On the use of graph centralities to compute generalized inverse of singular finite element operators: applications to the analysis of floating substructures

Christophe Bovet (1)

1 DMAS, ONERA, Université Paris Saclay [Châtillon]

This article introduces a robust and affordable method to compute nullspace and generalized inverse of finite element operators involved in dual domain decomposition methods. The methodology relies on the operator partial factorization and on the analysis of a well chosen Schur complement. The sparse linear operator is interpreted as a network and graph centrality measures are used to select the condensation variables. Eigen vector, Katz and Page Rank centralities are evaluated. An extension to deal with symmetric indefinite systems arising from mixed finite elements is also presented. The approach is assessed on highly heterogeneous problems and one industrial application is presented: the numerical homogenization of solid propellant.

Mots clés: Nullspace detection; Generalized inverse; FETI; Floating subdomain; Fixing-node; Graph centralities

Domaines: Sciences de l'ingénieur [physics]; Physique [physics]; Chimie

Christophe Bovet. On the use of graph centralities to compute generalized inverse of singular finite element operators: applications to the analysis of floating substructures. 2022. ⟨hal-03660559v2⟩