22,901 research outputs found
A specialized interior-point algorithm for huge minimum convex cost flows in bipartite networks
Research Report UPC-DEIO DR 2018-01. November 2018The computation of the Newton direction is the most time consuming step of interior-point methods. This direction was efficiently computed by a combination
of Cholesky factorizations and conjugate gradients in a specialized interior-point method for block-angular structured problems. In this work we apply this algorithmic approach to solve very large instances of minimum cost flows problems in bipartite networks, for convex objective functions with diagonal Hessians (i.e., either linear, quadratic or separable nonlinear objectives). After analyzing the theoretical properties of the interior-point method for this kind of problems, we provide extensive computational experiments with linear and quadratic instances of up to one billion arcs and 200 and five million nodes in each subset of the node partition. For linear and quadratic instances our approach is compared with the barriers algorithms of CPLEX (both standard path-following and homogeneous-self-dual); for linear instances it is also compared with the different algorithms of the state-of-the-art network flow solver LEMON (namely: network simplex, capacity scaling, cost scaling and cycle canceling).
The specialized interior-point approach significantly outperformed the other approaches in most of the linear and quadratic transportation instances tested. In particular, it always provided a solution within the time limit and it never exhausted the 192 Gigabytes of memory of the server used for the runs. For assignment problems the network algorithms in LEMON were the most efficient option.Peer ReviewedPreprin
Modeling transport of charged species in pore networks: solution of the Nernst-Planck equations coupled with fluid flow and charge conservation equations
A pore network modeling (PNM) framework for the simulation of transport of
charged species, such as ions, in porous media is presented. It includes the
Nernst-Planck (NP) equations for each charged species in the electrolytic
solution in addition to a charge conservation equation which relates the
species concentration to each other. Moreover, momentum and mass conservation
equations are adopted and there solution allows for the calculation of the
advective contribution to the transport in the NP equations.
The proposed framework is developed by first deriving the numerical model
equations (NMEs) corresponding to the partial differential equations (PDEs)
based on several different time and space discretization schemes, which are
compared to assess solutions accuracy. The derivation also considers various
charge conservation scenarios, which also have pros and cons in terms of speed
and accuracy. Ion transport problems in arbitrary pore networks were considered
and solved using both PNM and finite element method (FEM) solvers. Comparisons
showed an average deviation, in terms of ions concentration, between PNM and
FEM below with the PNM simulations being over times faster
than the FEM ones for a medium including about pores. The improved
accuracy is achieved by utilizing more accurate discretization schemes for both
the advective and migrative terms, adopted from the CFD literature. The NMEs
were implemented within the open-source package OpenPNM based on the iterative
Gummel algorithm with relaxation.
This work presents a comprehensive approach to modeling charged species
transport suitable for a wide range of applications from electrochemical
devices to nanoparticle movement in the subsurface
Deep Fluids: A Generative Network for Parameterized Fluid Simulations
This paper presents a novel generative model to synthesize fluid simulations
from a set of reduced parameters. A convolutional neural network is trained on
a collection of discrete, parameterizable fluid simulation velocity fields. Due
to the capability of deep learning architectures to learn representative
features of the data, our generative model is able to accurately approximate
the training data set, while providing plausible interpolated in-betweens. The
proposed generative model is optimized for fluids by a novel loss function that
guarantees divergence-free velocity fields at all times. In addition, we
demonstrate that we can handle complex parameterizations in reduced spaces, and
advance simulations in time by integrating in the latent space with a second
network. Our method models a wide variety of fluid behaviors, thus enabling
applications such as fast construction of simulations, interpolation of fluids
with different parameters, time re-sampling, latent space simulations, and
compression of fluid simulation data. Reconstructed velocity fields are
generated up to 700x faster than re-simulating the data with the underlying CPU
solver, while achieving compression rates of up to 1300x.Comment: Computer Graphics Forum (Proceedings of EUROGRAPHICS 2019),
additional materials: http://www.byungsoo.me/project/deep-fluids
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
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