Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of the time-domain PML problem for Maxwell's equations in a
  waveguide   This paper is concerned with the mathematical analysis of the time-domain
electromagnetic scattering problem in an infinite rectangular waveguide. A
transparent boundary condition is developed to reformulate the problem into an
equivalent initial boundary value problem in a bounded domain. The
well-posedness and stability are obtained for the reduced problem. The
perfectly matched layer method is studied to truncate the waveguide. It is
shown that the truncated problem attains a unique solution. Moreover, an
explicit error estimate is given between the solutions of the original
scattering problem and the truncated problem. Based on the estimate, the
stability and exponential convergence are established for the truncated
problem. The optimal bound is achieved for the error with explicit dependence
on the parameters of the perfectly matched layer.

31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics