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.
Highlights
Network structures are used to model a wide variety of phenomena, such as flow in porous media, traffic flows, elasticity of materials, body deformation in computer graphics, molecular dynamics, and fiber materials
The objective of this paper is to develop a numerical upscaling method for networks, circumventing the computational issues arising when materials of macrosize are considered
This paper concerns a quite general network model described by a connectivity matrix
Summary
Network structures are used to model a wide variety of phenomena, such as flow in porous media, traffic flows, elasticity of materials, body deformation in computer graphics, molecular dynamics, and fiber materials In these applications, the microscale behaviour determines the macroscale properties of the system. Multiscale methods applied to network problems are for instance investigated by Ewing [5] and Ilev et al [11] who study the heat conductivity of network materials and develop an upscaling method by solving the heat equation locally over small sub-domains. These local solutions are used to compute an effective global thermal conductivity tensor.
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