Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parareal computation of stochastic differential equations with
  time-scale separation: a numerical study   The parareal algorithm is known to allow for a significant reduction in wall
clock time for accurate numerical solutions by parallelising across the time
dimension. We present and test a micro-macro version of parareal, in which the
fine propagator is based on a (high-dimensional, slow-fast) stochastic
microscopic model, and the coarse propagator is based on a low-dimensional
approximate effective dynamics at slow time scales. At the microscopic level,
we use an ensemble of Monte Carlo particles, whereas the approximate coarse
propagator uses the (deterministic) Fokker-Planck equation for the slow degrees
of freedom. The required coupling between microscopic and macroscopic
representations of the system introduces several design options, specifically
on how to generate a microscopic probability distribution consistent with a
required macroscopic probability distribution and how to perform the
coarse-level updating of the macroscopic probability distribution in a
meaningful manner. We numerically study how these design options affect the
efficiency of the algorithm in a number of situations. The choice of the
coarse-level updating operator strongly impacts the result, with a superior
performance if addition and subtraction of the quantile function (inverse
cumulative distribution) is used. How microscopic states are generated has a
less pronounced impact, provided a suitable prior microscopic state is used.

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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: stat
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th