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Applying the swept rule for solving explicit partial differential equations on heterogeneous computing systems [article]

Daniel J. Magee, Anthony S. Walker, Kyle E. Niemeyer
2020 arXiv   pre-print
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]

Daniel Magee, Kyle E Niemeyer
2017 arXiv   pre-print
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

Daniel J. Magee, Kyle E. Niemeyer
2018 Journal of Computational Physics  
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

Constantinos I. Siettos
2011 Applied Mathematics and Computation  
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]

He Zhong, Hui Liu, Tao Cui, Lihua Shen, Bo Yang, Ruijian He, Zhangxin Chen
2018 arXiv   pre-print
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

Bernard J Geurts, Darryl D Holm
2006 Journal of Physics A: Mathematical and General  
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

Masoud Ghaderi Zefreh, Halvor M. Nilsen, Knut Andreas Lie, Xavier Raynaud, Florian Doster
2018 Computational Geosciences  
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]

Stefan Stoll
2014 Multifrequency Electron Paramagnetic Resonance  
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]

Sebastian Florez, Karen Alvarado, Marc Bernacki
2020 arXiv   pre-print
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

Alex Mogilner, David Odde
2011 Trends in Cell Biology  
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

Françoise Tisseur, Karl Meerbergen
2001 SIAM Review  
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]

Simon Foster, Jim Woodcock
2016 Lecture Notes in Computer Science  
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

E. Glen Weyl
2010 The American Economic Review  
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

Kata Kurgyis, Johannes Hommel, Bernd Flemisch, Rainer Helmig, Holger Ott
2021 Journal of Petroleum Science and Engineering  
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]

Jeffrey M. Wooldridge
2009 Complex Systems in Finance and Econometrics  
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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