Partitioning of Two-dimensional Nurbs Meshes for the Parallel Isogeometric Analysis

Isogeometric analysis is a quickly emerging alternative to the standard, polynomialbased finite element analysis. It is only the question of time, when it will be implemented into major software packages and will be intensively used by engineering community to the analysis of complex realistic problems. Computational demands of such analyses, that may likely exceed the capacity of a single computer, can be alleviated by performing the analyses in a parallel computing environment. However, parallel processing requires usually an appropriate decomposition of the investigated problem to individual processing units. In the case of the isogeometric analysis, the decomposition corresponds to the spatial partitioning of the underlying spatial discretization. While there are several matured graph-based decomposers which can be readily applied to the subdivision of finite element meshes, their use in the context of the isogeometric analysis is not straightforward because of a rather complicated construction of the graph corresponding to the computational isogeometric mesh. In this paper, a new technology for the construction of the dual graph of a two-dimensional NURBS-based (non-uniform rational B-spline) isogeometric mesh is introduced. This makes the partitioning of the isogeometric meshes for parallel processing accessible for the standard graph-based partitioning approaches.