Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient quadrature rules for finite element discretizations of
  nonlocal equations   In this paper we design efficient quadrature rules for finite element
discretizations of nonlocal diffusion problems with compactly supported kernel
functions. Two of the main challenges in nonlocal modeling and simulations are
the prohibitive computational cost and the nontrivial implementation of
discretization schemes, especially in three-dimensional settings. In this work
we circumvent both challenges by introducing a parametrized mollifying function
that improves the regularity of the integrand, utilizing an adaptive
integration technique, and exploiting parallelization. We first show that the
"mollified" solution converges to the exact one as the mollifying parameter
vanishes, then we illustrate the consistency and accuracy of the proposed
method on several two- and three-dimensional test cases. Furthermore, we
demonstrate the good scaling properties of the parallel implementation of the
adaptive algorithm and we compare the proposed method with recently developed
techniques for efficient finite element assembly.

26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph