Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sparsifying preconditioner for pseudospectral approximations of
  indefinite systems on periodic structures   This paper introduces the sparsifying preconditioner for the pseudospectral
approximation of highly indefinite systems on periodic structures, which
include the frequency-domain response problems of the Helmholtz equation and
the Schr\"odinger equation as examples. This approach transforms the dense
system of the pseudospectral discretization approximately into an sparse system
via an equivalent integral reformulation and a specially-designed sparsifying
operator. The resulting sparse system is then solved efficiently with sparse
linear algebra algorithms and serves as a reasonably accurate preconditioner.
When combined with standard iterative methods, this new preconditioner results
in small iteration counts. Numerical results are provided for the Helmholtz
equation and the Schr\"odinger in both 2D and 3D to demonstrate the
effectiveness of this new preconditioner.

11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con