Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New efficient time-stepping schemes for the anisotropic phase-field
  dendritic crystal growth model   In this paper, we propose and analyze a first-order and a second-order
time-stepping schemes for the anisotropic phase-field dendritic crystal growth
model. The proposed schemes are based on an auxiliary variable approach for the
Allen-Cahn equation and delicate treatment of the terms coupling the Allen-Cahn
equation and temperature equation. The idea of the former is to introduce
suitable auxiliary variables to facilitate construction of high order stable
schemes for a large class of gradient flows. We propose a new technique to
treat the coupling terms involved in the crystal growth model and introduce
suitable stabilization terms to result in totally decoupled schemes, which
satisfy a discrete energy law without affecting the convergence order. A
delicate implementation demonstrates that the proposed schemes can be realized
in a very efficient way. That is, it only requires solving four linear elliptic
equations and a simple algebraic equation at each time step. A detailed
comparison with existing schemes is given, and the advantage of the new schemes
are emphasized. As far as we know this is the first second-order scheme that is
totally decoupled, linear, unconditionally stable for the dendritic crystal
growth model with variable mobility parameter.

32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex