Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robust preconditioning for a mixed formulation of phase-field fracture
  problems   In this work, we consider fracture propagation in nearly incompressible and
(fully) incompressible materials using a phase-field formulation. We use a
mixed form of the elasticity equation to overcome volume locking effects and
develop a robust, nonlinear and linear solver scheme and preconditioner for the
resulting system. The coupled variational inequality system, which is solved
monolithically, consists of three unknowns: displacements, pressure, and
phase-field. Nonlinearities due to coupling, constitutive laws, and crack
irreversibility are solved using a combined Newton algorithm for the
nonlinearities in the partial differential equation and employing a primal-dual
active set strategy for the crack irreverrsibility constraint. The linear
system in each Newton step is solved iteratively with a flexible generalized
minimal residual method (GMRES). The key contribution of this work is the
development of a problem-specific preconditioner that leverages the
saddle-point structure of the displacement and pressure variable. Four
numerical examples in pure solids and pressure-driven fractures are conducted
on uniformly and locally refined meshes to investigate the robustness of the
solver concerning the Poisson ratio as well as the discretization and
regularization parameters.

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The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th