**
Partitioning of Two-dimensional NURBS Meshes**

for the Parallel Isogeometric Analysis

**
Daniel Rypl, Bořek Patzák
**

Department of Mechanics

Faculty of Civil Engineering

Czech Technical University in Prague

Thákurova 7, 166 29 Prague, Czech Republic

### Abstract:

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.