An accelerated staggered scheme for variational phase-field models of brittle fracture

Erlend Storvik*, Jakub Wiktor Both, Juan Michael Sargado, Jan Martin Nordbotten, Florin Adrian Radu

*Corresponding author for this work

    Research output: Contribution to journalJournal articleResearchpeer-review

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    There is currently an increasing interest in developing efficient solvers for variational phase-field models of brittle fracture. The governing equations for this problem originate from a constrained minimization of a non-convex energy functional, and the most commonly used solver is a staggered solution scheme. This is known to be robust compared to the monolithic Newton method, however, the staggered scheme often requires many iterations to converge when cracks are evolving. The focus of our work is to accelerate the solver through a scheme that sequentially applies Anderson acceleration and over-relaxation, switching back and forth depending on the residual evolution, and thereby ensuring a decreasing tendency. The resulting scheme takes advantage of the complementary strengths of Anderson acceleration and over-relaxation to make a robust and accelerating method for this problem. The new method is applied as a post-processing technique to the increments of the solver. Hence, the implementation merely requires minor modifications to already available software. Moreover, the cost of the acceleration scheme is negligible. The robustness and efficiency of the method are demonstrated through numerical examples.

    Original languageEnglish
    Article number113822
    JournalComputer Methods in Applied Mechanics and Engineering
    Number of pages19
    Publication statusPublished - 2021

    Bibliographical note

    Funding Information:
    This work is partially supported by the Research Council of Norway Project 250223 , the FracFlow project funded by Equinor, Norway through Akademiaavtalen, and by VISTA, Norway , a collaboration between the Norwegian Academy of Science and Letters and Equinor, project AdaSim #6367 .


    • Anderson acceleration
    • Nonlinear solver
    • Phase-field modeling
    • Relaxation
    • Staggered scheme
    • Variational brittle fracture


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