Fredrik Hellman: Numerical homogenization of geometric network models

Abstract: A sheet of paper can structural mechanically be modeled as an elasticity equation on a graph with edges for the fibers and vertices for the fiber contact points. To solve such a fine model, however, the vast number of degrees of freedom poses a computational challenge. In this talk, we apply a homogenization technique to the fine model and obtain an upscaled problem expressed on a coarser finite element mesh and that is easier to solve. The introduction and analysis of a Scott–Zhang type interpolation operator and the necessary assumptions on the network are the main theoretical contributions of this work.

This is a joint work with Axel Målqvist, Morgan Görtz and Gustav Kettil.