Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient numerical methods for computing the stationary states of phase
  field crystal models   Finding the stationary states of a free energy functional is an important
problem in phase field crystal (PFC) models. Many efforts have been devoted for
designing numerical schemes with energy dissipation and mass conservation
properties. However, most existing approaches are time-consuming due to the
requirement of small effective step sizes. In this paper, we discretize the
energy functional and propose efficient numerical algorithms for solving the
constrained non-convex minimization problem. A class of gradient based
approaches, which is the so-called adaptive accelerated Bregman proximal
gradient (AA-BPG) methods, is proposed and the convergence property is
established without the global Lipschitz constant requirements. A practical
Newton method is also designed to further accelerate the local convergence with
convergence guarantee. One key feature of our algorithms is that the energy
dissipation and mass conservation properties hold during the iteration process.
Moreover, we develop a hybrid acceleration framework to accelerate the AA-BPG
methods and most of existing approaches through coupling with the practical
Newton method. Extensive numerical experiments, including two three dimensional
periodic crystals in Landau-Brazovskii (LB) model and a two dimensional
quasicrystal in Lifshitz-Petrich (LP) model, demonstrate that our approaches
have adaptive step sizes which lead to a significant acceleration over many
existing methods when computing complex structures.

28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn