Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalized optimal fourth-order finite difference scheme for a 2D
  Helmholtz equation with the perfectly matched layer boundary condition   A crucial part of successful wave propagation related inverse problems is an
efficient and accurate numerical scheme for solving the seismic wave equations.
In particular, the numerical solution to a multi-dimensional Helmholtz equation
can be troublesome when the perfectly matched layer (PML) boundary condition is
implemented. In this paper, we present a general approach for constructing
fourth-order finite difference schemes for the Helmholtz equation with PML in
the two-dimensional domain based on point-weighting strategy. Particularly, we
develop two optimal fourth-order finite difference schemes, optimal
point-weighting 25p and optimal point-weighting 17p. It is shown that the two
schemes are consistent with the Helmholtz equation with PML. Moreover, an error
analysis for the numerical approximation of the exact wavenumber is provided.
Based on minimizing the numerical dispersion, we implement the refined choice
strategy for selecting optimal parameters and present refined point-weighting
25p and refined point-weighting 17p finite difference schemes. Furthermore,
three numerical examples are provided to illustrate the accuracy and
effectiveness of the new methods in reducing numerical dispersion.

19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc