Local enrichment of NURBS patches using a non-intrusive coupling strategy: Geometric details, local refinement, inclusion, fracture

Abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID : 14633 Highlights• We address the issue of modelling local phenomena in a NURBS patch with a global/local non-intrusive algorithm.• The approach provides simplicity and flexibility to treat any case of local enrichment in a NURBS patch.• We propose a strategy to handle non-conforming geometries.• We demonstrate the performance of the method on a range of two-dimensional linear elastic numerical examples. AbstractIn this work, we apply a non-intrusive global/local coupling strategy for the modelling of local phenomena in a NURBS patch. The idea is to consider the NURBS patch to be enriched as the global model. This results in a simple, flexible strategy: first, the global NURBS patch remains unchanged, which completely eliminates the need for costly re-parametrization procedures (even if the local domain is expected to evolve); then, easy merging of a linear NURBS code with any other existing robust codes suitable for the modelling of complex local behaviour is possible. The price to pay is the number of iterations of the non-intrusive solver but we show that this can be strongly reduced by means of acceleration techniques. The main development for NURBS is to be able to handle non-conforming geometries. Only slight changes in the implementation process, including the setting up of suitable quadrature rules for the evaluation of the interface reaction forces, are made in response to this issue. A range of numerical examples in two-dimensional linear elasticity are given to demonstrate the performance of the proposed methodology and its significant potential to treat any case of local enrichment in a NURBS patch simply.

Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches

“…As an application, we build in this section a non-intrusive algorithm to perform the local enrichment of a NURBS patch with the new mortar coupling. The performance of a non-intrusive strategy for the modeling of local behaviors in a NURBS patch has been demonstrated in Bouclier et al [36]. The goal here is to combine the advantages of a non-intrusive strategy with the property of higher-order continuity of the newly-developed mortar coupling.…”

“…This entails a considerable modeling effort, which is often as complex and time consuming as standard mesh generation. More details regarding this issue can be found in [29,36].…”

“…This feature is the basis of the non-overlapping domain decomposition methods developed for high performance computing on parallel computer architectures (see, e.g., [42][43][44]). In the same idea, such a property enables to build non-intrusive coupling algorithms for the modeling of local behaviors (see, e.g., [14,12,32,[34][35][36]). Several numerical codes can then be coupled in an iterative way with the exchange of only interface data to carry out the global/local simulation.…”

“…More recently, an extension in the NURBS context has been proposed in Bouclier et al [36] and has proved to be a good candidate for NURBS local enrichment (see Fig. 1 for illustration).…”

“…The advantages of such a computational strategy for NURBS are: the elimination of the re-construction of a numerical quadrature suitable to evaluate the global stiffness operator (even if the local area evolves), the possibility to assemble and factorize this global operator only once, the good conditioning of the systems to be solved, and the easy merging of a NURBS code with any other specific numerical codes. However, a classical Lagrange multiplier method was used in Bouclier et al [36] for the coupling and thus, only a C 0 continuity across the coupling interface was ensured. As a result, the goal of the present work is not only to develop a coupling method suitable with the higher-order continuity of NURBS, but also to be able to implement it in a non-intrusive way to perform NURBS local enrichment.…”