Dynamic and weighted stabilizations of the $L$-scheme applied to a phase-field model for fracture propagation

TL;DR

This paper introduces a dynamic stabilization approach for the L-scheme in a phase-field model of fracture propagation, significantly reducing iteration counts through adaptive parameter updates.

Contribution

It proposes a novel dynamic stabilization method for the L-scheme applied to coupled PDEs in fracture modeling, improving computational efficiency.

Findings

Dynamic stabilization reduces iteration numbers.

Adaptive parameters outperform constant stabilization.

Numerical tests validate efficiency gains.

Abstract

We consider a phase-field fracture propagation model, which consists of two (nonlinear) coupled partial differential equations. The first equation describes the displacement evolution, and the second is a smoothed indicator variable, describing the crack position. We propose an iterative scheme, the so-called $L$-scheme, with a dynamic update of the stabilization parameters during the iterations. Our algorithmic improvements are substantiated with two numerical tests. The dynamic adjustments of the stabilization parameters lead to a significant reduction of iteration numbers in comparison to constant stabilization values.