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Applying the swept rule for solving explicit partial differential equations on heterogeneous computing systems
[article]
2020
arXiv
pre-print
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These results show the potential effectiveness of the swept rule for different equations and numerical schemes on massively parallel computing systems that incur substantial latency costs. ...
This work extends the swept rule by targeting heterogeneous, CPU/GPU architectures representing current and future HPC systems. ...
All figures, and the data and plotting scripts necessary to reproduce them, for this article are available openly under the CC-BY license [30] . ...
arXiv:1811.08282v2
fatcat:pcdxjrayjbfvtbfqtae7f3yany
An initial investigation of the performance of GPU-based swept time-space decomposition
[article]
2017
arXiv
pre-print
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These phenomena are often described by mathematical models involving partial differential equations (PDEs) without exact solutions. ...
It shows significant improvement in the execution time of the PDE solvers in one dimension achieving speedups of 6-2x for large and small problem sizes respectively compared to naive GPU versions and 7 ...
We also gratefully acknowledge the support of NVIDIA Corporation with the donation of the Tesla K40 GPU used for this research. ...
arXiv:1612.02495v2
fatcat:szemkhqylrgqxivgt2hudj7age
Accelerating solutions of one-dimensional unsteady PDEs with GPU-based swept time–space decomposition
2018
Journal of Computational Physics
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2017 pre-print arXiv:1705.03162v1 fatcat:zs4t2mp7rzd6rgi2q5yjlwdf4mOther Versions
However, for a more sophisticated one-dimensional system of equations discretized with a second-order finite-volume scheme, the swept rule performs 1.2--1.9× worse than a standard implementation for all ...
The expedient design of precision components in aerospace and other high-tech industries requires simulations of physical phenomena often described by partial differential equations (PDEs) without exact ...
We also gratefully acknowledge the support of NVIDIA Corporation with the donation of the Tesla K40 GPU used for this research. ...
doi:10.1016/j.jcp.2017.12.028
fatcat:h2mj5hz3kfgmhghf6tqvrrnyqa
Equation-Free multiscale computational analysis of individual-based epidemic dynamics on networks
2011
Applied Mathematics and Computation
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2010 pre-print arXiv:1012.4194v1 fatcat:bpnetonn6ra2tjtcv37oarisfi
systems-level, analysis. ...
In this work it is shown how one can exploit the Equation Free approach and optimization methods such as Simulated Annealing to bridge detailed individual-based epidemic simulation with coarse-grained, ...
Such models can be explored using powerful analysis techniques for ordinary and partial differential equations. ...
doi:10.1016/j.amc.2011.05.067
fatcat:prvv2mqd5bbd3hdn2mleasvgai
Numerical Simulations of Polymer Flooding Process in Porous Media on Distributed-memory Parallel Computers
[article]
2018
arXiv
pre-print
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Numerical experiments show that, on one hand, computed results match those from the commercial simulator, Schlumberger-Eclipse, which is widely applied by the petroleum industry, and, on the other hand ...
Darcy's law is employed to model the behavoir of a fluid in porous media, and the upstream finite difference (volume) method is applied to discretize the mass conservation equations. ...
The research is partly supported by NSERC/Energi Simulation Chair, Alberta Innovate Chair, IBM Thomas J.Watson Research Center, and the Frank and Sarah Meyer FCMG Collaboration Centre for Visualization ...
arXiv:1807.05298v3
fatcat:d6hkzl44wfel7kl6buuxlyidia
Commutator errors in large-eddy simulation
2006
Journal of Physics A: Mathematical and General
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The performance of this commutator error parametrization is illustrated for the one-dimensional Burgers equation. ...
For situations in which the dynamical consequences of the commutator errors are significant, e.g., near solid boundaries, explicit similarity modelling for the commutator errors is proposed, including ...
Acknowledgments BJG would like to acknowledge support from the Los Alamos Turbulence Working Group and Center for Nonlinear Studies. ...
doi:10.1088/0305-4470/39/9/015
fatcat:4swgjunpcvadzfivsdfap5znyq
Streamline simulation of a reactive advective flow with discontinuous flux function
2018
Computational Geosciences
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The method consists of a front-tracking solver that uses the Riemann solutions of the underlying set of hyperbolic partial differential equations. ...
In addition to the discontinuities stemming from the nonlinearities of the flux function, the flux function for the corresponding advection reaction equation also admits discontinuities for a heterogeneous ...
Eric Mackay for the fruitful discussions. ...
doi:10.1007/s10596-018-9771-3
fatcat:dbc3ordigjhwff55irjskcpdxi
Computational Modeling and Least-Squares Fittingof EPR Spectra
[chapter]
2014
Multifrequency Electron Paramagnetic Resonance
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These classical equations cannot be applied to spin systems with more than one spin- 1 2 . In general, quantum dynamics has to be applied. ...
For the transition intensities and linewidths, the same expressions as for the field-swept case apply, except for one important difference: The frequency-to-field conversion factor, discussed in Section ...
doi:10.1002/9783527672431.ch3
fatcat:pnq4q7yf2nfkzauekoirawvcma
A new front-tracking Lagrangian model for the modeling of dynamic and post-dynamic recrystallization
[article]
2020
arXiv
pre-print
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The computational performance will be evaluated for the DRX and PDRX mechanisms and compared to a classical Finite Element (FE) framework using a Level-Set (LS) formulation. ...
of the domains are driven by selective local remeshing operations performed on the Finite Element (FE) mesh. ...
Acknowledgments The authors thank the ArcelorMittal, ASCOMETAL, AUBERT & DUVAL, CEA, FRAMATOME, SAFRAN, TIMET, Constellium and TRANSVALOR companies and the ANR for their financial support through the DIGIMU ...
arXiv:2009.08368v1
fatcat:rbugic2tanaw5outhhityg5g5a
Modeling cellular processes in 3D
2011
Trends in Cell Biology
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Paul for donating Figure 1d . ...
Modeling approaches in 3D Partial differential equation (PDE) modeling: a traditional tool of applied mathematics widely used in modeling spatially explicit processes in biology [59] . ...
Notably, unlike most 3D computational models using the agent-based approach, the authors [48] employed computationally demanding numerical analysis of partial differential equations describing actin-myosin ...
doi:10.1016/j.tcb.2011.09.007
pmid:22036197
pmcid:PMC3221767
fatcat:pw7pt7egwnaljb5tffqktld4zy
The Quadratic Eigenvalue Problem
2001
SIAM Review
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We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. ...
Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. ...
Coyette for their valuable comments on the manuscript that led to many improvements. ...
doi:10.1137/s0036144500381988
fatcat:4hyhd4sfmnbdjdoe3336k3kajq
Towards Verification of Cyber-Physical Systems with UTP and Isabelle/HOL
[chapter]
2016
Lecture Notes in Computer Science
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In this paper, we outline our vision for building verification tools for Cyber-Physical Systems based on Hoare and He's Unifying Theories of Programming (UTP) and interactive proof technology in Isabelle ...
We conclude by reflecting on how tools are linked by unifying theories. This paper is dedicated to Bill Roscoe on the occasion of his 60th birthday. ...
We would like to thank our colleagues Ana Cavalcanti, Bernhard Thiele, and Burkhart Wolff for their collaboration on this work. ...
doi:10.1007/978-3-319-51046-0_3
fatcat:5spfjc633vdt3g5hfeupfjgaoq
A Price Theory of Multi-Sided Platforms
2010
The American Economic Review
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Note that the assumption of twice-continuous differentiability actually rules out all of the one-dimensional cases. ...
THEOREM 4: If f A , f B and c exhibit strict 2SC then for any C A and C B a solution to equation (6) for both I is the unique platform's optimal price. ...
doi:10.1257/aer.100.4.1642
fatcat:qholfzrkurcr7iqumlgko4vdeu
EXPLICIT CONTINUUM SCALE MODELING OF LOW-SALINITY MECHANISMS
2021
Journal of Petroleum Science and Engineering
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By assuming sets of input parameters, we show that there is a minimum required core length dependent on the dispersion of the chemical flooding front dominated by sample heterogeneity. ...
Understanding the influence of injection water composition on the displacement efficiency has been a longstanding issue in reservoir engineering; a reduction of the injection water salinity can lead to ...
Credit author statement
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the ...
doi:10.1016/j.petrol.2020.108336
fatcat:2pxnkug2ezhg5lwyfxocx6bnva
Econometrics: Panel Data Methods
[chapter]
2009
Complex Systems in Finance and Econometrics
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Nevertheless,
(3.1) The traditional starting point for studying (3.1) is to rule out correlation between the
3 ) 3 so the j are partial effects holding fixed the unobserved heterogeneity (and ...
solutions. ...
doi:10.1007/978-1-4419-7701-4_12
fatcat:xx7earjkknga3ntpab2cgmffza
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