  Non-linear phase field models are increasingly used for the simulation of
fracture propagation models. The numerical simulation of fracture networks of
realistic size requires the efficient parallel solution of large coupled
non-linear systems. Although in principle efficient iterative multi-level
methods for these types of problems are available, they are not widely used in
practice due to the complexity of their parallel implementation.
  Here, we present Utopia, which is an open-source C++ library for parallel
non-linear multilevel solution strategies. Utopia provides the advantages of
high-level programming interfaces while at the same time a framework to access
low-level data-structures without breaking code encapsulation. Complex
numerical procedures can be expressed with few lines of code, and evaluated by
different implementations, libraries, or computing hardware. In this paper, we
investigate the parallel performance of our implementation of the recursive
multilevel trust-region (RMTR) method based on the Utopia library. RMTR is a
globally convergent multilevel solution strategy designed to solve non-convex
constrained minimization problems. In particular, we solve pressure-induced
phase-field fracture propagation in large and complex fracture networks.
Solving such problems is deemed challenging even for a few fractures, however,
here we are considering networks of realistic size with up to 1000 fractures.
