Numerical homogenization of spatial network models
Artikel i vetenskaplig tidskrift, 2024

We present and analyze a methodology for numerical homogenization of spatial networks models, e.g. heat conduction and linear deformation in large networks of slender objects, such as paper fibers. The aim is to construct a coarse model of the problem that maintains high accuracy also on the micro-scale. By solving decoupled problems on local subgraphs we construct a low dimensional subspace of the solution space with good approximation properties. The coarse model of the network is expressed by a Galerkin formulation and can be used to perform simulations with different source and boundary data, at a low computational cost. We prove optimal convergence to the micro-scale solution of the proposed method under mild assumptions on the homogeneity, connectivity, and locality of the network on the coarse scale. The theoretical findings are numerically confirmed for both scalar-valued (heat conduction) and vector-valued (linear deformation) models.

Algebraic connectivity

Multiscale method

Discrete model

Localized orthogonal decomposition

Network model

Upscaling

Författare

Fredrik Edelvik

Stiftelsen Fraunhofer-Chalmers Centrum för Industrimatematik

Morgan Görtz

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Stiftelsen Fraunhofer-Chalmers Centrum för Industrimatematik

Fredrik Hellman

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Gustav Kettil

Stiftelsen Fraunhofer-Chalmers Centrum för Industrimatematik

Axel Målqvist

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Computer Methods in Applied Mechanics and Engineering

0045-7825 (ISSN)

Vol. 418 116593

Ämneskategorier

Teknisk mekanik

Beräkningsmatematik

Transportteknik och logistik

DOI

10.1016/j.cma.2023.116593

Mer information

Senast uppdaterat

2023-11-22