Residual error based adaptive mesh refinement with the non-intrusive patch algorithm

Abstract

This paper deals with the introduction of mesh refinement techniques within the non-intrusive patch process. For this, an ad hoc residual based explicit error estimator is built, which is adapted to a multi-scale solution, associated with those non-intrusive mesh refinement technique. Moreover, to reduce the global cost of the process, one introduces an estimate of the convergence error of the non-intrusive algorithm, which allows to reduce the number of iterations. This method is discussed and illustrated in various numerical examples.

Non-invasive global–local coupling as a Schwarz domain decomposition method: acceleration and generalization

“…This problem would appear much later on the residual which only involves nodal computations (which can be manipulated in double precision). Note that this problem was encountered in other studies based on Abaqus software [37] but not in studies which used Code_Aster for example [41]. Table 2 compares the duration of the computation.…”

“…A more extensive numerical campaign should be conducted with varying position for the interfaces and different element sizes (so that situations where the transfers behave poorly may be encountered). Moreover, the method shall also be assessed in term of discretization error in the spirit of [41].…”

A Nitsche-based non-intrusive coupling strategy for global/local isogeometric structural analysis

“…It seems that a criterion based on a coupling error of 10 −4 is a bit too demanding. To go further, a suitable error estimator should be implemented to stop the iterative algorithm at the right time [67]. Such an estimator, which should be extended to the case of NURBS, goes beyond the scope of this work, and we chose to stop the algorithm at 10 −4 in the following.…”

Non Intrusive Global/Local Coupling Techniques in Solid Mechanics: An Introduction to Different Coupling Strategies and Acceleration Techniques

“…A number of other applications and extensions have been proposed: use of XFEM at the local scale Passieux et al (2013), treatment of non-matching interfaces Liu et al (2014), coupling between a global plate model and 3D parts for bolted assemblies Guguin et al (2014), geometrically non conforming coupling Guinard et al (2018), multiscale time and space computation in explicit dynamic Bettinotti et al (2014) with implementation in Abaqus Explicit for the analysis of delamination under impact Bettinotti et al (2017), non-invasive domain decomposition approach Duval et al (2016). Mesh refinement based on error estimation may also be cast in the proposed non-intrusive framework Duval et al (2018).…”