Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structure and properties of linear sampling method for perfectly
  conducting, arc-like cracks   We consider the imaging of arbitrary shaped, arc-like perfectly conducting
cracks located in the two-dimensional homogeneous space via linear sampling
method. Based on the structure of eigenvectors of so-called Multi Static
Response (MSR) matrix, we discover the relationship between imaging functional
adopted in the linear sampling method and Bessel function of integer order of
the first kind. This relationship tells us that why linear sampling method
works for imaging of perfectly conducting cracks in either Transverse Magnetic
(Dirichlet boundary condition) and Transverse Electric (Neumann boundary
condition), and explains its certain properties. Furthermore, we suggest
multi-frequency imaging functional, which improves traditional linear sampling
method. Various numerical experiments are performed for supporting our
explores.

26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat