Super-Localized Orthogonal Decomposition Method for Heterogeneous Linear Elasticity
Abstract
We present the Super-Localized Orthogonal Decomposition (SLOD) method for the numerical homogenization of linear elasticity problems with multiscale microstructures modeled by a heterogeneous coefficient field without any periodicity or scale separation assumptions. Compared to the established Localized Orthogonal Decomposition (LOD) and its linear localization approach, SLOD achieves significantly improved sparsity properties through a nonlinear superlocalization technique, leading to computationally efficient solutions with significantly less oversampling - without compromising accuracy. We generalize the method to vector-valued problems and provide a supporting numerical analysis. We also present a scalable implementation of SLOD using the deal.II finite element library, demonstrating its feasibility for high-performance simulations. Numerical experiments illustrate the efficiency and accuracy of SLOD in addressing key computational challenges in multiscale elasticity.
Cite
@article{arxiv.2501.05193,
title = {Super-Localized Orthogonal Decomposition Method for Heterogeneous Linear Elasticity},
author = {Camilla Belponer and José C. Garay and Peter Munch and Daniel Peterseim},
journal= {arXiv preprint arXiv:2501.05193},
year = {2025}
}