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

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