Abstract
Non-linear phase field models are increasingly used for the simulation of fracture propagation problems. 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.
Highlights
Fractures and fracture networks strongly affect the hydraulic and mechanical response of the underground
We presented the first open-source code for numerical modelling of large-scale phase-field fracture simulations using the recursive multilevel trust-region (RMTR) method
Our implementation of the phase-field fracture model employs an expression template-based assembler designed for structured grids and 2D/3D tensorproduct finite elements
Summary
Fractures and fracture networks strongly affect the hydraulic and mechanical response of the underground. Several aforementioned codes are implemented on the top of parallel finite element framework Their applicability to solve large-scale problems is often limited by the convergence and the scaling properties of a utilized solution strategy. In order to avoid changes in high-level algorithms, such as non-linear solution strategies, or finite element analysis, several application codes are developed on top of a portable interface that fits many current and possibly future requirements [e.g., PETSc (Balay et al 1997, 2019), Trilinos (Heroux et al 2003), and Kokkos (Edwards et al 2014)] Software libraries such as Deal.II (Bangerth et al 2007), LibMesh (Kirk et al 2006), Dune (Blatt et al 2016), and MOOSE (Gaston et al 2009) rely on high level abstractions on top of existing linear algebra and non-linear solution strategies codes, and allow choosing, to some degree, the underlying implementation. We provide concluding remarks and describe future work (Sect. 7)
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