Analytical Comparison of Two Multiscale Coupling Methods for Nonlinear Solid Mechanics

Abstract

The aim of this work is to compare two existing multilevel computational approaches coming from two different families of multiscale methods in a nonlinear solid mechanics framework. A locally adaptive multigrid method and a numerical homogenization technique are considered. Both classes of methods aim to enrich a global model representing the structure’s behavior with more sophisticated local models depicting fine localized phenomena. It is clearly shown that even being developed with different vocations, such approaches reveal several common features. The main conceptual difference relying on the scale separation condition has finally a limited influence on the algorithmic aspects. Hence, this comparison enables to highlight a unified framework for multiscale coupling methods.

A unified framework for the computational comparison of adaptive mesh refinement strategies for all-quadrilateral and all-hexahedral meshes: Locally adaptive multigrid methods versus h-adaptive methods

“…Moreover, local multigrid methods are really generic and flexible as they enable us to change the refinement ratio, the model, the solver, etc. between each level (see for example [18,50,51]).…”