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arXiv · 2501.05193

Super-Localized Orthogonal Decomposition Method for Heterogeneous Linear Elasticity

Camilla Belponer·José C. Garay·Peter Munch·Daniel Peterseim
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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.

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Camilla Belponer, José C. Garay, Peter Munch, Daniel Peterseim. 2025-01-09. Super-Localized Orthogonal Decomposition Method for Heterogeneous Linear Elasticity. https://arxiv.org/abs/2501.05193

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