Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal artificial boundary conditions based on second-order correctors
  for three dimensional random elliptic media   We are interested in numerical algorithms for computing the electrical field
generated by a charge distribution localized on scale $\ell$ in an infinite
heterogeneous medium, in a situation where the medium is only known in a box of
diameter $L\gg\ell$ around the support of the charge. We propose a boundary
condition that with overwhelming probability is (near) optimal with respect to
scaling in terms of $\ell$ and $L$, in the setting where the medium is a sample
from a stationary ensemble with a finite range of dependence (set to be unity
and with the assumption that $\ell \gg 1$). The boundary condition is motivated
by quantitative stochastic homogenization that allows for a multipole expansion
[BGO20].
  This work extends [LO21] from two to three dimensions, and thus we need to
take quadrupoles, next to dipoles, into account. This in turn relies on
stochastic estimates of second-order, next to first-order, correctors. These
estimates are provided for finite range ensembles under consideration, based on
an extension of the semi-group approach of [GO15].

10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom