4,958 research outputs found
An asymptotic induced numerical method for the convection-diffusion-reaction equation
A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method
Justification of lubrication approximation: an application to fluid/solid interactions
We consider the stationary Stokes problem in a three-dimensional fluid domain
with non-homogeneous Dirichlet boundary conditions. We assume that
this fluid domain is the complement of a bounded obstacle in a
bounded or an exterior smooth container . We compute sharp asymptotics
of the solution to the Stokes problem when the distance between the obstacle
and the container boundary is small
A multi-resolution approximation for massive spatial datasets
Automated sensing instruments on satellites and aircraft have enabled the
collection of massive amounts of high-resolution observations of spatial fields
over large spatial regions. If these datasets can be efficiently exploited,
they can provide new insights on a wide variety of issues. However, traditional
spatial-statistical techniques such as kriging are not computationally feasible
for big datasets. We propose a multi-resolution approximation (M-RA) of
Gaussian processes observed at irregular locations in space. The M-RA process
is specified as a linear combination of basis functions at multiple levels of
spatial resolution, which can capture spatial structure from very fine to very
large scales. The basis functions are automatically chosen to approximate a
given covariance function, which can be nonstationary. All computations
involving the M-RA, including parameter inference and prediction, are highly
scalable for massive datasets. Crucially, the inference algorithms can also be
parallelized to take full advantage of large distributed-memory computing
environments. In comparisons using simulated data and a large satellite
dataset, the M-RA outperforms a related state-of-the-art method.Comment: 23 pages; to be published in Journal of the American Statistical
Associatio
A Quantitative Study of Pure Parallel Processes
In this paper, we study the interleaving -- or pure merge -- operator that
most often characterizes parallelism in concurrency theory. This operator is a
principal cause of the so-called combinatorial explosion that makes very hard -
at least from the point of view of computational complexity - the analysis of
process behaviours e.g. by model-checking. The originality of our approach is
to study this combinatorial explosion phenomenon on average, relying on
advanced analytic combinatorics techniques. We study various measures that
contribute to a better understanding of the process behaviours represented as
plane rooted trees: the number of runs (corresponding to the width of the
trees), the expected total size of the trees as well as their overall shape.
Two practical outcomes of our quantitative study are also presented: (1) a
linear-time algorithm to compute the probability of a concurrent run prefix,
and (2) an efficient algorithm for uniform random sampling of concurrent runs.
These provide interesting responses to the combinatorial explosion problem
On the least exponential growth admitting uncountably many closed permutation classes
We show that the least exponential growth of counting functions which admits
uncountably many closed permutation classes lies between 2^n and
(2.33529...)^n.Comment: 13 page
- …