  We propose a quality-based optimization strategy to reduce the total number
of degrees of freedom associated to a discrete problem defined over a polygonal
tessellation with the Virtual Element Method. The presented Quality
Agglomeration algorithm relies only on the geometrical properties of the
problem polygonal mesh, agglomerating groups of neighboring elements. We test
this approach in the context of fractured porous media, in which the generation
of a global conforming mesh on a Discrete Fracture Network leads to a
considerable number of unknowns, due to the presence of highly complex
geometries and the significant size of the computational domains. We show the
efficiency and the robustness of our approach, applied independently on each
fracture for different network configurations, exploiting the flexibility of
the Virtual Element Method in handling general polygonal elements.
