744 research outputs found
Robust globally divergence-free weak Galerkin finite element methods for natural convection problems
This paper proposes and analyzes a class of weak Galerkin (WG) finite element
methods for stationary natural convection problems in two and three dimensions.
We use piecewise polynomials of degrees k, k-1, and k(k>=1) for the velocity,
pressure, and temperature approximations in the interior of elements,
respectively, and piecewise polynomials of degrees l, k, l(l = k-1,k) for the
numerical traces of velocity, pressure and temperature on the interfaces of
elements. The methods yield globally divergence-free velocity solutions.
Well-posedness of the discrete scheme is established, optimal a priori error
estimates are derived, and an unconditionally convergent iteration algorithm is
presented. Numerical experiments confirm the theoretical results and show the
robustness of the methods with respect to Rayleigh number.Comment: 32 pages, 13 figure
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Training a Large-Scale 3D Convolutional Neural Network Predicting Human Intelligence in Adolescent Brain Cognitive Development Study
ThumbNet: One Thumbnail Image Contains All You Need for Recognition
Although deep convolutional neural networks (CNNs) have achieved great
success in computer vision tasks, its real-world application is still impeded
by its voracious demand of computational resources. Current works mostly seek
to compress the network by reducing its parameters or parameter-incurred
computation, neglecting the influence of the input image on the system
complexity. Based on the fact that input images of a CNN contain substantial
redundancy, in this paper, we propose a unified framework, dubbed as ThumbNet,
to simultaneously accelerate and compress CNN models by enabling them to infer
on one thumbnail image. We provide three effective strategies to train
ThumbNet. In doing so, ThumbNet learns an inference network that performs
equally well on small images as the original-input network on large images.
With ThumbNet, not only do we obtain the thumbnail-input inference network that
can drastically reduce computation and memory requirements, but also we obtain
an image downscaler that can generate thumbnail images for generic
classification tasks. Extensive experiments show the effectiveness of ThumbNet,
and demonstrate that the thumbnail-input inference network learned by ThumbNet
can adequately retain the accuracy of the original-input network even when the
input images are downscaled 16 times
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