Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planewave density interpolation methods for 3D Helmholtz boundary
  integral equations   This paper introduces planewave density interpolation methods for the
regularization of weakly singular, strongly singular, hypersingular and nearly
singular integral kernels present in 3D Helmholtz surface layer potentials and
associated integral operators. Relying on Green's third identity and pointwise
interpolation of density functions in the form of planewaves, these methods
allow layer potentials and integral operators to be expressed in terms of
integrand functions that remain smooth (at least bounded) regardless the
location of the target point relative to the surface sources. Common
challenging integrals that arise in both Nystr\"om and boundary element
discretization of boundary integral equation, can then be numerically evaluated
by standard quadrature rules that are irrespective of the kernel singularity.
Closed-form and purely numerical planewave density interpolation procedures are
presented in this paper, which are used in conjunction with Chebyshev-based
Nystr\"om and Galerkin boundary element methods. A variety of numerical
examples---including problems of acoustic scattering involving multiple
touching and even intersecting obstacles, demonstrate the capabilities of the
proposed technique.

28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org