Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmonic density interpolation methods for high-order evaluation of
  Laplace layer potentials in 2D and 3D   We present an effective harmonic density interpolation method for the
numerical evaluation of singular and nearly singular Laplace boundary integral
operators and layer potentials in two and three spatial dimensions. The method
relies on the use of Green's third identity and local Taylor-like
interpolations of density functions in terms of harmonic polynomials. The
proposed technique effectively regularizes the singularities present in
boundary integral operators and layer potentials, and recasts the latter in
terms of integrands that are bounded or even more regular, depending on the
order of the density interpolation. The resulting boundary integrals can then
be easily, accurately, and inexpensively evaluated by means of standard
quadrature rules. A variety of numerical examples demonstrate the effectiveness
of the technique when used in conjunction with the classical trapezoidal rule
(to integrate over smooth curves) in two-dimensions, and with a Chebyshev-type
quadrature rule (to integrate over surfaces given as unions of non-overlapping
quadrilateral patches) in three-dimensions.

16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex