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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/ fatcat:h2mj5hz3kfgmhghf6tqvrrnyqa

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

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

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] .  ...  It is not difficult to formulate a model in 3D, but solving its partial differential equations, which are the most powerful and developed mathematical tool, is very taxing; the amounts of memory, disk  ... 
doi:10.1016/j.tcb.2011.09.007 pmid:22036197 pmcid:PMC3221767 fatcat:pw7pt7egwnaljb5tffqktld4zy

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.  ...  Here, we solve the Riemann problem for the governing nonlinear hyperbolic system with a discontinuous flux function.  ...  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.  ...  The expressions are based on solving the equation ΔE − ℏ mw = 0 with a Taylor expansion in a iso of the Breit-Rabi expression for ΔE.  ... 
doi:10.1002/9783527672431.ch3 fatcat:pnq4q7yf2nfkzauekoirawvcma

The Quadratic Eigenvalue Problem

Françoise Tisseur, Karl Meerbergen
2001 SIAM Review  
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.  ...  We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques.  ...  Coyette for their valuable comments on the manuscript that led to many improvements.  ... 
doi:10.1137/s0036144500381988 fatcat:4hyhd4sfmnbdjdoe3336k3kajq

A fast computational model for the electrophysiology of the whole human heart [article]

Giulio Del Corso, Roberto Verzicco, Francesco Viola
2021 arXiv   pre-print
In this study we present a novel computational model for unprecedented simulations of the whole cardiac electrophysiology.  ...  three different cellular models, the Courtemanche model [1] for the atrial myocytes, the Stewart model [2] for the Purkinje Network and the ten Tusscher-Panfilov model [3] for the ventricular myocytes.  ...  The resulting bidomain model [27, 28] thus consists of the coupling between a system of reaction–diffusion partial differential equations (PDEs, governing the potential propagation in the media) and a  ... 
arXiv:2112.12854v1 fatcat:k5qrbpcoojhbpdruad4ew3ppoe

Phage mobility is a core determinant of phage-bacteria coexistence in biofilms [article]

Matthew Simmons, Knut Drescher, Carey Nadell, Vanni Bucci
2016 bioRxiv   pre-print
It is also unclear how the ecological dynamics of phages and their hosts depend on the biological and physical properties of the biofilm environment.  ...  Many bacteria are adapted for attaching to surfaces and for building complex communities, termed biofilms. The biofilm mode of life is predominant in bacterial ecology.  ...  Acknowledgements We are grateful to Ann Tate, Petra Klepac, and Adrian de Froment for comments on the manuscript.  ... 
doi:10.1101/086462 fatcat:spdurt7dr5bdrlisjh2bmo3z2u

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

Control-volume method for numerical simulation of two-phase immiscible flow in two- and three-dimensional discrete-fractured media

J. E. P. Monteagudo, A. Firoozabadi
2004 Water Resources Research  
The system of partial differential equations is decoupled and solved using the implicit-pressure, explicitsaturation (IMPES) approach.  ...  This concept, which is often referred to as the discrete-fracture model, has a significant effect on the reduction of computational time.  ...  With this procedure, the system of equations (1) -(4) is reduced to two partial differential equations: Àr Á l n þ l w ð Þ r F w ð Þ À r Ál n rF c ð ÞÀ q n þ q w ð Þ¼0 ð8Þ @ fS w ð Þ @t À r Á l w rF w  ... 
doi:10.1029/2003wr002996 fatcat:6nhrvviqrjadhjezobmjosdrgq

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.  ...  As the appendix shows, the only assumption needed for the analysis is smoothness with regards to movements of the boundary of a set, that is sufficient conditions for the Leibnitz Integral Rule to apply  ... 
doi:10.1257/aer.100.4.1642 fatcat:qholfzrkurcr7iqumlgko4vdeu

Semi-analytic geometry with R-functions

Vadim Shapiro
2007 Acta Numerica  
Functions for shapes with corners Many equations of a rectangle How does one write an equation for a rectangle?  ...  operate on real-valued inequalities as differentiable logic operations; the resulting theory solves the inverse problem of analytic geometry and has a wide range of applications, with particular emphasis  ...  The responsibility for any errors and omissions lies solely with the author.  ... 
doi:10.1017/s096249290631001x fatcat:o7cqokkg4vfyngm5kj32kwtk7q
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