Parallel Integral Curves 111
ulation checkpoints are not saved frequently enough for accurate time-varying
flow visualization.
Besides the need to visualize large data sizes, the ability to trace a large
number of particles is also a valuable asset. While hundreds of thousands or
millions of particles may be too many for human viewing, a very dense field
of streamlines or pathlines may be necessary for accurate follow-on analysis.
The accuracy of techniques such as identifying Lagrangian coherent structures
and querying geometric features of field lines relies on a dense field of particle
traces.
6.4 Conclusion
IC methods are a foundational technique that have proven to be a valuable
tool in the analysis and understanding of complex flow with scientific simula-
tions. These techniques provide a powerful framework for a variety of specific
analyses, including streamlines, pathlines, streak lines, stream surfaces, as well
as advanced Lagrangian techniques, such as Finite Time Lyapunov Exponents
(FTLE), and Lagrangian Cohrent Structures.
Due to the complexities of IC calculation in a parallel, distributed mem-
ory setting, as outlined in 6.2, it is clear that there is no optimal algorithm
suitable for all types of vector fields, seeding scenarios, and data set sizes. The
complexities of parallel IC computations are likely to stress the entire system,
including compute, memory, communication, and I/O. This chapter outlined
several different algorithms that showed a good scalability on large computing
resources, on very large data sets, that were built on the standard algorithms
for parallelization across both seeds and data. These include the dynamic
workload monitoring of both particles and data blocks and the rebalancing of
work among the available processors, efficient data structures, and techniques
for maximizing the efficiency of communication between processors.
112 High Performance Visualization
References
[1] David Camp, Hank Childs, Amit Chourasia, Christoph Garth, and Ken-
neth I. Joy. Evaluating the Benefits of An Extended Memory Hierarchy
for Parallel Streamline Algorithms. In Proceedings of the IEEE Sym-
posium on Large-Scale Data Analysis and Visualization (LDAV), pages
57–64. IEEE Press, October 2011.
[2] C. Cardall, A. Razoumov, E. Endeve, E. Lentz, and A. Mezzacappa.
Toward Five-Dimensional Core-Collapse Supernova Simulations. Journal
of Physics: Conference Series, 16:390–394, 2005.
[3] E. Endeve, C. Y. Cardall, R. D. Budiardja, and A. Mezzacappa. Gen-
eration of Strong Magnetic Fields in Axisymmetry by the Stationary
Accretion Shock Instability. ArXiv e-prints, November 2008.
[4] E. Hairer, S. P. Nørsett, and G. Wanner. Solving Ordinary Differential
Equations I, Second Edition, volume 8 of Springer Series in Comput.
Mathematics. Springer-Verlag, 1993.
[5] G Haller. Lagrangian Structures and the Rate of Strain in a Partition of
Two-Dimensional Turbulence. Physics of Fluids, 13(11):3365, 2001.
[6] Hari Krishnan, Christoph Garth, and Kenneth I. Joy. Time and
Streak Surfaces for Flow Visualization in Large Time-Varying Data Sets.
15(6):1267–1274, October 2009.
[7] Francois Lekien, Shawn C. Shadden, and Jerrold E. Marsden. Lagrangian
Coherent Structures in N-Dimensional Systems. 48(6):065404, 2007.
[8] Tony McLoughlin, Robert S. Laramee, Ronald Peikert, Frits H. Post,
and Min Chen. Over Two Decades of Integration-Based, Geometric Flow
Visualization. In EuroGraphics 2009 - State of the Art Reports, pages
73–92. Eurographics Association, April 2009.
[9] Tom Peterka, Wesley Kendall, David Goodell, Boonthanome Nouanesen-
gsey, Han-Wei Shen, Jian Huang, Kenneth Moreland, Rajeev Thakur,
and Robert Ross. Performance of Communication Patterns for Extreme-
Scale Analysis and Visualization. Journal of Physics, Conference Series,
pages 194–198, July 2010.
[10] Tom Peterka, Robert Ross, Boonthanome Nouanesengsey, Teng-Yok Lee,
Han-Wei Shen, Wesley Kendall, and Jian Huang. A Study of Parallel
Particle Tracing for Steady-State and Time-Varying Flow Fields. In Pro-
ceedings of IPDPS 11, pages 577–588, Anchorage AK, 2011.
Parallel Integral Curves 113
[11] Dave Pugmire, Hank Childs, Christoph Garth, Sean Ahern, and Gun-
ther H. Weber. Scalable Computation of Streamlines on Very Large
Datasets. In Proceedings of Supercomputing (SC09), Portland, OR, USA,
November 2009.
[12] C.R. Sovinec, A.H. Glasser, T.A. Gianakon, D.C. Barnes, R.A. Nebel,
S.E. Kruger, S.J. Plimpton, A. Tarditi, M.S. Chu, and the NIM-
ROD Team. Nonlinear Magnetohydrodynamics with High-order Finite
Elements. Journal of Computational Physics, 195:355, 2004.
[13] Hongfeng Yu, Chaoli Wang, and Kwan-Liu Ma. Parallel Hierarchical
Visualization of Large Time-Varying 3D Vector Fields. In Proceedings of
Supercomputing (SC07), 2007.
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.