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

Abstract

The non-invasive global-local coupling algorithm is revisited and shown to realize a simple implementation of the optimized non-overlapping Schwarz domain decomposition method. This connection is used to propose and compare several acceleration techniques, and to extend the approach to non conforming meshes.

A parallel non-invasive mixed domain decomposition - Implementation and applications to mechanical assemblies

“…It was applied as a complete solver in [21]. In fact the global/local coupling can be 1 viewed as a particular non-overlapping Schwarz method where the Robin condition is managed by a coarse representation of the domain [22]. This idea was exploited in [23] for the non-invasive implementation of the Latin method, the Robin conditions being simulated through the addition of elements on the interfaces of subdomains.…”

Space/time global/local noninvasive coupling strategy: Application to viscoplastic structures

“…The strategy makes use of three computational models based on the decomposition of the reference problem as explained in [17] The global/local (GL) solution is defined on the reference model (Ω R = Ω L ∪ Ω C ) as the replacement of the global solution by the local one in the zone of interest:…”

“…The local and auxiliary analysis are computed in parallel thus the use of the auxiliary model does not add computational time to the general algorithm. The algorithm is a stationary iteration; its convergence can be proved under very general hypothesis (see [28] for a proof with weak hypothesis and [17] for the registration of the method amongst Schwarz alternating methods for which many convergence results exist). In the general case, relaxation may have to be used to ensure convergence by modifying (13) as follows: P i+1 = P i + ωr i , with ω small enough.…”

Global Local Analysis with Robin Parameters: Applications to Crack Propagation in 2D and 3D Models

“…The global/local approach consists in an iterative Dirichlet-Neumann algorithm where an iteration is composed of two steps: (1) a problem on the local model with Dirichlet boundary conditions on the interface, and (2) a problem on the global model with Neumann boundary conditions on the interface. Links with Optimized Schwarz domain decomposition methods can be found in [9]. The global/local framework has been generalized to a domain decomposition method with a complete covering local model [3].…”