A Weak Galerkin Finite Element Method for Second-Order Elliptic Problems. (arXiv:1104.2897v1 [math.NA])

A Weak Galerkin Finite Element Method for Second-Order Elliptic Problems. (arXiv:1104.2897v1 [math.NA]): "

In this paper, authors shall introduce a finite element method by using a
weakly defined gradient operator over discontinuous functions with
heterogeneous properties. The use of weak gradients and their approximations
results in a new concept called {\em discrete weak gradients} which is expected
to play important roles in numerical methods for partial differential
equations. This article intends to provide a general framework for operating
differential operators on functions with heterogeneous properties. As a
demonstrative example, the discrete weak gradient operator is employed as a
building block to approximate the solution of a model second order elliptic
problem, in which the classical gradient operator is replaced by the discrete
weak gradient. The resulting numerical approximation is called a weak Galerkin
(WG) finite element solution. It can be seen that the weak Galerkin method
allows the use of totally discontinuous functions in the finite element
procedure. For the second order elliptic problem, an optimal order error
estimate in both a discrete $H^1$ and $L^2$ norms are established for the
corresponding weak Galerkin finite element solutions. A superconvergence is
also observed for the weak Galerkin approximation.

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Parallel calculation of the median and order statistics on GPUs with application to robust regression. (arXiv:1104.2732v1 [cs.DC])

Parallel calculation of the median and order statistics on GPUs with application to robust regression. (arXiv:1104.2732v1 [cs.DC]): "

We present and compare various approaches to a classical selection problem on
Graphics Processing Units (GPUs). The selection problem consists in selecting
the $k$-th smallest element from an array of size $n$, called $k$-th order
statistic. We focus on calculating the median of a sample, the $n/2$-th order
statistic. We introduce a new method based on minimization of a convex
function, and show its numerical superiority when calculating the order
statistics of very large arrays on GPUs. We outline an application of this
approach to efficient estimation of model parameters in high breakdown robust
regression.

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