Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Floquet-Bloch transform based numerical method for scattering from
  locally perturbed periodic surfaces   Scattering problems for periodic structures have been studied a lot in the
past few years. A main idea for numerical solution methods is to reduce such
problems to one periodicity cell. In contrast to periodic settings, scattering
from locally perturbed periodic surfaces is way more challenging. In this
paper, we introduce and analyze a new numerical method to simulate scattering
from locally perturbed periodic structures based on the Bloch transform. As
this transform is applied only in periodic domains, we firstly rewrite the
scattering problem artificially in a periodic domain. With the help of the
Bloch transform, we secondly transform this problem into a coupled family of
quasiperiodic problems posed in the periodicity cell. A numerical scheme then
approximates the family of quasiperiodic solutions (we rely on the finite
element method) and backtransformation provides the solution to the original
scattering problem. In this paper, we give convergence analysis and error
bounds for a Galerkin discretization in the spatial and the quasiperiodicity's
unit cells. We also provide a simple and efficient way for implementation that
does not require numerical integration in the quasiperiodicity, together with
numerical examples for scattering from locally perturbed periodic surfaces
computed by this scheme.

7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin