Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isoparametric singularity extraction technique for 3D potential problems
  in BEM   To solve boundary integral equations for potential problems using collocation
Boundary Element Method (BEM) on smooth curved 3D geometries, an analytical
singularity extraction technique is employed. By adopting the isoparametric
approach, curved geometries that are represented by mapped rectangles or
triangles from the parametric domain are considered. The singularity extraction
on the governing singular integrals can be performed either as an operation of
subtraction or division, each having some advantages. A particular series
expansion of a singular kernel about a source point is investigated. The series
in the intrinsic coordinates consists of functions of a type $R^p x^q y^r$,
where $R$ is a square root of a quadratic bivariate homogeneous polynomial,
corresponding to the first fundamental form of a smooth surface, and $p,q,r$
are integers, satisfying $p\leq -1$ and $q,r \geq 0$. By extracting more terms
from the series expansion of the singular kernel, the smoothness of the
regularized kernel at the source point can be increased. Analytical formulae
for integrals of such terms are obtained from antiderivatives of $R^p x^q y^r$,
using recurrence formulae, and by evaluating them at the edges of rectangular
or triangular parametric domains. Numerical tests demonstrate that the
singularity extraction technique can be a useful prerequisite for a numerical
quadrature scheme to obtain accurate evaluations of the governing singular
integrals in 3D collocation BEM.

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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: stat