Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A robust monolithic solver for phase-field fracture integrated with
  fracture energy based arc-length method and under-relaxation   The phase-field fracture free-energy functional is non-convex with respect to
the displacement and the phase field. This results in a poor performance of the
conventional monolithic solvers like the Newton-Raphson method. In order to
circumvent this issue, researchers opt for the alternate minimization
(staggered) solvers. Staggered solvers are robust for the phase-field based
fracture simulations as the displacement and the phase-field sub-problems are
convex in nature. Nevertheless, the staggered solver requires very large number
of iterations (of the order of thousands) to converge. In this work, a robust
monolithic solver is presented for the phase-field fracture problem. The solver
adopts a fracture energy-based arc-length method and an adaptive
under-relaxation scheme. The arc-length method enables the simulation to
overcome critical points (snap-back, snap-through instabilities) during the
loading of a specimen. The use of an under-relaxation scheme stabilizes the
solver by preventing the divergence due to an ill-behaving stiffness matrix.
The efficiency of the proposed solver is further amplified with an adaptive
mesh refinement scheme based on PHT-splines within the framework of
isogeometric analysis. The numerical examples presented in the manuscript
demonstrates the efficacy of the solver. All the codes and data-sets
accompanying this work will be made available on GitHub
(https://github.com/rbharali/IGAFrac).

37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph