# Matrix-free multigrid solvers for phase-field fracture problems

@article{Jodlbauer2020MatrixfreeMS, title={Matrix-free multigrid solvers for phase-field fracture problems}, author={Daniel Jodlbauer and Ulrich Langer and Thomas Wick}, journal={Computer Methods in Applied Mechanics and Engineering}, year={2020} }

In this work, we present a framework for the matrix-free solution to a monolithic quasi-static phase-field fracture model with geometric multigrid methods. Using a standard matrix based approach within the Finite Element Method requires lots of memory, which eventually becomes a serious bottleneck. A matrix-free approach overcomes this problems and greatly reduces the amount of required memory, allowing to solve larger problems on available hardware. One key challenge is concerned with the…

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## 11 Citations

Parallel matrix-free higher-order finite element solvers for phase-field fracture problems

- Computer Science, MathematicsArXiv
- 2020

A new parallel matrix-free monolithic multigrid preconditioner for phase-field fracture models and the most time-consuming part in the discrete version of the primal-dual active set (semi-smooth Newton) algorithm is proposed.

Preconditioning strategies for vectorial finite element linear systems arising from phase-field models for fracture mechanics

- Computer Science
- 2021

To improve convergence rates, consequently time to solution, of the conjugate gradient method applied to crack propagation problems, different preconditioning strategies are analyzed, tuned, and discussed.

An efficient and robust monolithic approach to phase-field quasi-static brittle fracture using a modified Newton method

- Computer ScienceArXiv
- 2021

This work proposes an efficient and robust fully monolithic solver for phase-field fracture using a modified Newton method with inertia correction and an energy line-search, and demonstrates the gains in efficiency obtained with this approach.

pfm-cracks: A parallel-adaptive framework for phase-field fracture propagation

- Computer ScienceSoftw. Impacts
- 2020

The main features of the parallel-adaptive open-source framework for solving phase-field fracture problems called pfm-cracks, which allows for dimension-independent programming in two- and three-dimensional settings, are described.

A quasi-monolithic phase-field description for orthotropic anisotropic fracture with adaptive mesh refinement and primal–dual active set method

- Materials ScienceEngineering Fracture Mechanics
- 2021

Abstract In this work, thermodynamically consistent phase-field fracture frameworks for transversely isotropic and orthotropic settings are proposed. We formulate an anisotropic crack phase-field via…

Fast implicit solvers for phase-field fracture problems on heterogeneous microstructures

- Computer Science
- 2020

Fast and memory-efficient FFT-based implicit solution methods for small-strain phase-field crack problems for microstructured brittle materials are studied, and the heavy ball scheme is identified as particularly powerful.

A survey of fracture, delamination, crack branching and crack deflection in composites using a novel framework for phase field fracture

- 2021

Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have…

Bayesian inversion for unified ductile phase-field fracture

- Computer Science, MathematicsComputational Mechanics
- 2021

A Bayesian inversion framework for ductile fracture is developed to provide accurate knowledge regarding the effective mechanical parameters and synthetic and experimental observations are used to estimate the posterior density of the unknowns.

A mixed phase-field fracture model for crack propagation in punctured EPDM strips

- Materials Science, Computer ScienceArXiv
- 2021

Abstract In this work, we present crack propagation experiments evaluated by digital image correlation (DIC) for a carbon black filled ethylene propylene diene monomer rubber (EPDM) and numerical…

Block structured adaptive mesh refinement and strong form elasticity approach to phase field fracture with applications to delamination, crack branching and crack deflection

- Physics
- 2021

Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have…

## References

SHOWING 1-10 OF 117 REFERENCES

Parallel matrix-free higher-order finite element solvers for phase-field fracture problems

- Computer Science, MathematicsArXiv
- 2020

A new parallel matrix-free monolithic multigrid preconditioner for phase-field fracture models and the most time-consuming part in the discrete version of the primal-dual active set (semi-smooth Newton) algorithm is proposed.

A matrix‐free approach for finite‐strain hyperelastic problems using geometric multigrid

- Computer Science, Mathematics
- 2019

The application of matrix-free methods to finite-strain solid mechanics is promising, and it is concluded that it is possible to develop numerically efficient implementations that are independent of the hyperelastic constitutive law.

A line search assisted monolithic approach for phase-field computing of brittle fracture

- Computer Science
- 2016

This work proposes a faster and equally accurate approach for quasi-static phase-field computing of (brittle) fracture using a monolithic solution scheme which is accompanied by a novel line search procedure to overcome the iterative convergence issues of non-convex minimization.

A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach

- Mathematics
- 2015

Abstract In this paper, we consider phase-field based fracture propagation in elastic media. The main purpose is the development of a robust and efficient numerical scheme. To enforce crack…

Linear and nonlinear solvers for variational phase-field models of brittle fracture

- Mathematics, Computer Science
- 2015

This paper reformulates alternate minimization as a nonlinear Gauss-Seidel iteration and employs over-relaxation to accelerate its convergence, and forms efficient preconditioners for the solution of the linear subproblems arising in both alternate minimizations and in Newton's method.

An Error-Oriented Newton/Inexact Augmented Lagrangian Approach for Fully Monolithic Phase-Field Fracture Propagation

- Mathematics, Computer ScienceSIAM J. Sci. Comput.
- 2017

The purpose of this work is the development of a fully monolithic solution algorithm for quasi-static phase-field fracture propagation using an adaptive error-oriented Newton algorithm which works as an inner loop within an inexact augmented Lagrangian iteration.

A fast and robust iterative solver for nonlinear contact problems using a primal‐dual active set strategy and algebraic multigrid

- Mathematics
- 2007

For extending the usability of implicit FE codes for large-scale forming simulations, the computation time has to be decreased dramatically. In principle this can be achieved by using iterative…

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

- Mathematics, Computer SciencePAMM
- 2018

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.

A phase-field model for fractures in nearly incompressible solids

- MathematicsComputational Mechanics
- 2019

Within this work, we develop a phase-field description for simulating fractures in nearly incompressible materials. It is well-known that low-order approximations generally lead to volume-locking…

Modified Newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation

- Mathematics
- 2017

Abstract Our goal in this work is to develop and compare modified Newton methods for fully monolithic quasi-static brittle phase-field fracture propagation. In variational phase-field fracture, a…