Numerical upscaling of discrete network models

TL;DR

This paper introduces a numerical multiscale method for discrete networks that efficiently captures coarse-scale behavior, especially in complex or random structures, and demonstrates its application to paper-based material modeling.

Contribution

The paper presents a novel multiscale numerical method for discrete networks, enabling accurate coarse representations and convergence in complex network problems.

Findings

Achieves optimal order convergence rates.

Effectively models complex network structures.

Successfully applied to paper-based materials.

Abstract

In this paper a numerical multiscale method for discrete networks is presented. The method gives an accurate coarse scale representation of the full network by solving sub-network problems. The method is used to solve problems with highly varying connectivity or random network structure, showing optimal order convergence rates with respect to the mesh size of the coarse representation. Moreover, a network model for paper-based materials is presented. The numerical multiscale method is applied to solve problems governed by the presented network model.