Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multilevel Hierarchical Decomposition of Finite Element White Noise with
  Application to Multilevel Markov Chain Monte Carlo   In this work we develop a new hierarchical multilevel approach to generate
Gaussian random field realizations in an algorithmically scalable manner that
is well-suited to incorporate into multilevel Markov chain Monte Carlo (MCMC)
algorithms. This approach builds off of other partial differential equation
(PDE) approaches for generating Gaussian random field realizations; in
particular, a single field realization may be formed by solving a
reaction-diffusion PDE with a spatial white noise source function as the
righthand side. While these approaches have been explored to accelerate forward
uncertainty quantification tasks, e.g. multilevel Monte Carlo, the previous
constructions are not directly applicable to multilevel MCMC frameworks which
build fine scale random fields in a hierarchical fashion from coarse scale
random fields. Our new hierarchical multilevel method relies on a hierarchical
decomposition of the white noise source function in $L^2$ which allows us to
form Gaussian random field realizations across multiple levels of
discretization in a way that fits into multilevel MCMC algorithmic frameworks.
After presenting our main theoretical results and numerical scaling results to
showcase the utility of this new hierarchical PDE method for generating
Gaussian random field realizations, this method is tested on a four-level MCMC
algorithm to explore its feasibility.

23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an