Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Randomized sampling for basis functions construction in generalized
  finite element methods   In the framework of generalized finite element methods for elliptic equations
with rough coefficients, efficiency and accuracy of the numerical method depend
critically on the use of appropriate basis functions. This work explores
several random sampling strategies that construct approximations to the optimal
set of basis functions of a given dimension, and proposes a quantitative
criterion to analyze and compare these sampling strategies. Numerical evidence
shows that the best results are achieved by two strategies, Random Gaussian and
Smooth boundary sampling.

11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th