Scalable multiscale-spectral GFEM with an application to composite aero-structures

In this paper, the first large-scale application of multiscale-spectral generalized finite element
methods (MS-GFEM) to composite aero-structures is presented. The crucial novelty lies in the
introduction of A-harmonicity in the local approximation spaces, which in contrast to Babuška
and Lipton (2011) [30] is enforced more efficiently via a constraint in the local eigenproblems.
This significant modification leads to excellent approximation properties, which turn out to be
essential to capture accurately material strains and stresses with a low dimensional approximation
space, hence maximizing model order reduction. The implementation of the framework in the
Distributed and Unified Numerics Environment (DUNE) software package, as well as a detailed
description of all components of the method are presented and exemplified on a composite
laminated beam under compressive loading. The excellent parallel scalability of the method,
as well as its superior performance compared to the related, previously introduced GenEO
method are demonstrated on two realistic application cases, including a C-shaped wing spar
with complex geometry. ... mehrFurther, by allowing low-cost approximate solves for closely related
models or geometries this efficient, novel technology provides the basis for future applications in
optimization or uncertainty quantification on challenging problems in composite aero-structures.