Non-intrusive Coupling: Recent Advances and Scalable Nonlinear Domain Decomposition

Abstract

This paper provides a detailed review of the global/local non-intrusive coupling algorithm. Such method allows to alter a global finite element model, without actually modifying its corresponding numerical operator. We also look into improvements of the initial algorithm (QuasiNewton and dynamic relaxation), and provide comparisons based on several relevant test cases. Innovative examples and advanced applications of the non-intrusive coupling algorithm are provided, granting a handy framework for both researchers and engineers willing to make use of such process. Finally, a novel nonlinear domain decomposition method is derived from the global/local non-intrusive coupling strategy, without the need to use a parallel code or software. Such method being intended to large scale analysis, we show its scalability. Jointly, an efficient high level Message Passing Interface coupling framework is also proposed, granting an universal and flexible way for easy software coupling. A sample code is also given.

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

“…The starting point in the derivation of a non-intrusive strategy in the sense of [11,29,30] is to weakly formulate the coupling problem (4)-(5) with a Lagrange multiplier approach. The development of the non-intrusive coupling formulation is not the subject of this section.…”

“…An iterative coupling technique is used to perform the substitution in an exact but non-intrusive way: only interface data are transmitted from one model to the other and the global stiffness operator remains unchanged (independently of the shape of the local domain). This strategy has been applied in FEM for the modelling of crack propagation [11], for the modelling of localized uncertainties [28], for 3D-plate coupling [29] and for nonlinear domain decomposition [30]. Let us note that this methodology, involving the coupling of a global model and a local model in an iterative manner, has similarities with some hierarchical global/local methods in FEM: for example, the Chimera method [31], the method of finite element patches [32], numerical zoom [33] or the hp − d method [34][35][36].…”

“…In this paper, we propose an application of the non-intrusive technique [27,12,11,[28][29][30] to the NURBS context. The idea is to take the NURBS patch to be enriched as the global model.…”

“…For this purpose, an exact NURBS domain is simply constructed from the NURBS trimming curve in the case of a geometric detail while the quadrature rule used for the local model is transposed within the global NURBS patch in the case of real (covered) local models. With regard to coupling, an application of the conventional Lagrange multiplier approach to non-conforming geometries is employed to meet the non-intrusive constraint in the sense of [11,29,30]. Acceleration techniques, such as techniques based on Aitken's Delta Squared method or a Quasi-Newton method (see, e.g., [30]), are also implemented in the present situation, which results in a significant reduction of the number of iterations of the non-intrusive algorithm.…”

“…Moreover, it is important to notice that the algorithm proposed here is the standard one and that its convergence may be slow in certain situations. To answer this issue, acceleration techniques, such as based on an Aitken's Delta Squared method or a Quasi-Newton method, can be applied to the present situation from the existing developments in classical FEM (see, e.g., [30]). Numerical experiments to account for this point will be carried out in Section 4.…”