  Fiber network modeling can be used for studying mechanical properties of
paper. The individual fibers and the bonds in-between constitute a detailed
representation of the material. However, detailed microscale fiber network
models must be resolved with efficient numerical methods. In this work, a
numerical multiscale method for discrete network models is proposed that is
based on the localized orthogonal decomposition method [arXiv:1810.05059]. The
method is ideal for these network problems, because it reduces the maximum size
of the problem, it is suitable for parallelization, and it can effectively
solve fracture propagation.
  The problem analyzed in this work is the nodal displacement of a fiber
network given an applied load. This problem is formulated as a linear system
that is solved by using the aforementioned multiscale method. To solve the
linear system, the multiscale method constructs a low-dimensional solution
space with good approximation properties. The method is observed to work well
for unstructured fiber networks, with optimal rates of convergence obtainable
for highly localized configurations of the method.
