Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Phase-Field Description for Pressurized and Non-Isothermal Propagating
  Fractures   In this work, we extend a phase-field approach for pressurized fractures to
non-isothermal settings. Specifically, the pressure and the temperature are
given quantities and the emphasis is on the correct modeling of the interface
laws between a porous medium and the fracture. The resulting model is augmented
with thermodynamical arguments and then analyzed from a mechanical perspective.
The numerical solution is based on a robust semi-smooth Newton approach in
which the linear equation systems are solved with a generalized minimal
residual method and algebraic multigrid preconditioning. The proposed modeling
and algorithmic developments are substantiated with different examples in two-
and three dimensions. We notice that for some of these configurations
manufactured solutions can be constructed, allowing for a careful verification
of our implementation. Furthermore, crack-oriented predictor-corrector
adaptivity and a parallel implementation are used to keep the computational
cost reasonable. Snapshots of iteration numbers show an excellent performance
of the nonlinear and linear solution algorithms. Lastly, for some tests, a
computational analysis of the effects of strain-energy splitting is performed,
which has not been undertaken to date for similar phase-field settings
involving pressure, fluids or non-isothermal effects.

12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci