Parallel solution, adaptivity, computational convergence, and open-source code of 2d and 3d pressurized phase-field fracture problems

TL;DR

This paper introduces a scalable, open-source parallel solver for 2D and 3D phase-field fracture problems, demonstrating optimal convergence and adaptive mesh refinement benefits in computational simulations.

Contribution

It provides a novel parallel implementation with adaptive mesh refinement for phase-field fracture models, ensuring optimal scaling and convergence in 2D and 3D simulations.

Findings

Optimal scaling of linear solver with algebraic multigrid

Adaptive mesh refinement improves convergence rates

Finite domain size influences functional evaluations

Abstract

We present a scalable, parallel implementation of a solver for the solution of a phase-field model for quasi-static brittle fracture. The code is available as open source. Numerical solutions in 2d and 3d with adaptive mesh refinement show optimal scaling of the linear solver based on algebraic multigrid, and convergence of the phase-field model towards exact values of functionals of interests such as the crack opening displacement or the total crack volume. In contrast to uniform refinement, adaptive mesh refinement allows us to recover optimal convergence rates for the non-smooth solutions encountered in typical test problems. We also present numerical studies of the influence of the finite domain size on functional evaluations used to approximate the infinite domain.