Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A model reduction method for multiscale elliptic PDEs with random
  coefficients using an optimization approach   In this paper, we propose a model reduction method for solving multiscale
elliptic PDEs with random coefficients in the multiquery setting using an
optimization approach. The optimization approach enables us to construct a set
of localized multiscale data-driven stochastic basis functions that give
optimal approximation property of the solution operator. Our method consists of
the offline and online stages. In the offline stage, we construct the localized
multiscale data-driven stochastic basis functions by solving an optimization
problem. In the online stage, using our basis functions, we can efficiently
solve multiscale elliptic PDEs with random coefficients with relatively small
computational costs. Therefore, our method is very efficient in solving target
problems with many different force functions. The convergence analysis of the
proposed method is also presented and has been verified by the numerical
simulation.

6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex