An adapted deflated conjugate gradient solver for robust extended/generalised finite element solutions of large scale, 3D crack propagation problems

TL;DR

This paper introduces an adapted deflated conjugate gradient solver that accelerates the solution of large-scale 3D crack propagation problems in fracture mechanics by combining deflation with block-Jacobi preconditioning.

Contribution

It develops a novel preconditioning approach that enriches the deflation space with enrichment functions and combines it with block-Jacobi preconditioning for improved efficiency.

Findings

Significant speed-up in solving large-scale crack propagation problems.

Effective removal of low and high frequency error components.

Outperforms traditional linear solvers in tested scenarios.

Abstract

An adapted deflation preconditioner is employed to accelerate the solution of linear systems resulting from the discretization of fracture mechanics problems with well-conditioned extended/generalized finite elements. The deflation space typically used for linear elasticity problems is enriched with additional vectors, accounting for the enrichment functions used, thus effectively removing low frequency components of the error. To further improve performance, deflation is combined, in a multiplicative way, with a block-Jacobi preconditioner, which removes high frequency components of the error as well as linear dependencies introduced by enrichment. The resulting scheme is tested on a series of non-planar crack propagation problems and compared to alternative linear solvers in terms of performance.