Construction of weighted dual graphs of NURBS-based isogeometric meshes

Isogeometric analysis has been recently introduced as a viable alternative to the standard, polynomial-based finite element analysis. Similarly to the finite element method, isogeometric solution of complex engineering problems may lead to computationally very demanding analysis, demands of which can be alleviated by performing it in a parallel computing environment. While the actual parallelization of the isogeometric computational code resembles methodologically very much the parallelization of the finite element code, the construction of the appropriate domain decomposition of the isogeometric mesh is rather complicated compared to the partitioning of the finite element mesh. The aim of this paper is to introduce a new methodology for the construction of a weighted dual graph of a two-dimensional NURBS-based isogeometric mesh that can be decomposed by standard graph-based partitioning approaches.