Revisiting the evaluation of in situ lagrangian analysis
Abstract
In situ usage of Lagrangian techniques has proven to be superior with respect to emerging supercomputing trends than the traditional Eulerian approach for scientific flow analysis. However, previous studies have not informed two key points: (1) the accuracy of the post hoc interpolated trajectory as a whole and (2) the spatiotemporal tradeoffs involved when using Lagrangian analysis. With this short paper, we address these points. We first conduct a more comprehensive evaluation via additional accuracy metrics tailored for evaluating Lagrangian trajectories. Second, we provide an understanding of the configurations where the Lagrangian approach works well by studying spatiotemporal tradeoffs. In addition, our study highlights the effects of error propagation and accumulation when performing Lagrangian interpolation for large numbers of steps. We believe our study is significant for better understanding the use of in situ Lagrangian techniques, as well as serving as a baseline for future Lagrangian research.
References
[1]
{ACG*14} Agranovsky A., Camp D., Garth C., Bethel E. W., Joy K. I., Childs H.: Improved post hoc flow analysis via lagrangian representations. In Large Data Analysis and Visualization (LDAV), 2014 IEEE 4th Symposium on (2014), IEEE, pp. 67--75. 1, 2, 3
[2]
{AGJ11} Agranovsky A., Garth C., Joy K. I.: Extracting flow structures using sparse particles. In VMV (2011), pp. 153--160. 2
[3]
{AJO*14} Ahrens J., Jourdain S., O'Leary P., Patchett J., Rogers D. H., Petersen M.: An image-based approach to extreme scale in situ visualization and analysis. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (2014), IEEE Press, pp. 424--434. 1
[4]
{Atk08} Atkinson K. E.: An introduction to numerical analysis. John Wiley & Sons, 2008. 2
[5]
{BAA*16} Bauer A. C., Abbasi H., Ahrens J., Childs H., Geveci B., Klasky S., Moreland K., O'Leary P., Vishwanath V., Whitlock B., et al.: In situ methods, infrastructures, and applications on high performance computing platforms. In Computer Graphics Forum (2016), vol. 35, Wiley Online Library, pp. 577--597. 1
[6]
{BCT01} Brummell N., Cattaneo F., Tobias S.: Linear and nonlinear dynamo properties of time-dependent abc flows. Fluid Dynamics Research 28, 4 (2001), 237--265. 2
[7]
{BJ15} Bujack R., Joy K. I.: Lagrangian representations of flow fields with parameter curves. In Large Data Analysis and Visualization (LDAV), 2015 IEEE 5th Symposium on (2015), IEEE, pp. 41--48. 2, 3
[8]
{CBJ16} Chandler J., Bujack R., Joy K. I.: Analysis of error in interpolation-based pathline tracing. In Proceedings of the Eurographics / IEEE VGTC Conference on Visualization: Short Papers (2016), EuroVis '16, Eurographics Association, pp. 1--5.
[9]
{CK90} Cash J. R., Karp A. H.: A variable order runge-kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software (TOMS) 16, 3 (1990), 201--222. 2
[10]
{COJ15} Chandler J., Obermaier H., Joy K. I.: Interpolation-based pathline tracing in particle-based flow visualization. IEEE transactions on visualization and computer graphics 21, 1 (2015), 68--80. 2
[11]
{FMT*11} Fabian N., Moreland K., Thompson D., Bauer A. C., Marion P., Gevecik B., Rasquin M., Jansen K. E.: Theparaview coprocessing library: A scalable, general purpose in situ visualization library. In Large Data Analysis and Visualization (LDAV), 2011 IEEE Symposium on (2011), IEEE, pp. 89--96. 1
[12]
{GGTH07} Garth C., Gerhardt F., Tricoche X., Hans H.: Efficient computation and visualization of coherent structures in fluid flow applications. IEEE Transactions on Visualization and Computer Graphics 13, 6 (2007), 1464--1471. 2
[13]
{GLT*09} Garth C., Li G.-S., Tricoche X., Hansen C. D., Hagen H.: Visualization of coherent structures in transient 2d flows. In Topology-Based Methods in Visualization II. Springer, 2009, pp. 1--13. 2
[14]
{Hal00} Haller G.: Finding finite-time invariant manifolds in two-dimensional velocity fields. Chaos: An Interdisciplinary Journal of Non-linear Science 10, 1 (2000), 99--108. 2
[15]
{Hal01} Haller G.: Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D: Nonlinear Phenomena 149, 4 (2001), 248--277. 2
[16]
{HBJG16} Hummel M., Bujack R., Joy K. I., Garth C.: Error Estimates for Lagrangian Flow Field Representations. In EuroVis 2016 - Short Papers (2016), The Eurographics Association. 2, 4
[17]
{HSW11} Hlawatsch M., Sadlo F., Weiskopf D.: Hierarchical line integration. IEEE transactions on visualization and computer graphics 17, 8 (2011), 1148--1163. 2
[18]
{HY00} Haller G., Yuan G.: Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D: Nonlinear Phenomena 147, 3 (2000), 352--370. 2
[19]
{MOM*11} Moreland K., Oldfield R., Marion P., Jourdain S., Podhorszki N., Vishwanath V., Fabian N., Docan C., Parashar M., Hereld M., et al.: Examples of in transit visualization. In Proceedings of the 2nd international workshop on Petascal data analytics: challenges and opportunities (2011), ACM, pp. 1--6. 1
[20]
{OWW15} Orf L., Wilhelmson R., Wicker L.: Visualization of a simulated Long-Track EF5 tornado embedded within a supercell thunderstorm. Parallel Comput. 0, 0 (2015). In press. 2
[21]
{Sch02} Schatzmann M.: Numerical Analysis: A Mathematical Introduction. Oxford University Press, New York, USA, 2002. 2
[22]
{SP07} Sadlo F., Peikert R.: Efficient visualization of lagrangian coherent structures by filtered amr ridge extraction. IEEE Transactions on Visualization and Computer Graphics 13, 6 (2007), 1456--1463. 2
[23]
{SRP11} Sadlo F., Rigazzi A., Peikert R.: Time-dependent visualization of lagrangian coherent structures by grid advection. In Topological Methods in Data Analysis and Visualization. Springer, 2011, pp. 151--165. 2
[24]
{SXM16} Sauer F., Xie J., Ma K.-L.: A combined eulerian-lagrangian data representation for large-scale applications. IEEE Transactions on Visualization and Computer Graphics (2016). 2
[25]
{VHP11} Vishwanath V., Hereld M., Papka M. E.: Toward simulation-time data analysis and i/o acceleration on leadership-class systems. In Large Data Analysis and Visualization (LDAV), 2011 IEEE Symposium on (2011), IEEE, pp. 9--14. 1
[26]
{WFM11} Whitlock B., Favre J. M., Meredith J. S.: Parallel in situ coupling of simulation with a fully featured visualization system. In Proceedings of the 11th Eurographics Conference on Parallel Graphics and Visualization (2011), EGPGV '11, Eurographics Association, pp. 101--109. 1
[27]
{YWG*10} Yu H., Wang C., Grout R. W., Chen J. H., Ma K.-L.: In situ visualization for large-scale combustion simulations. IEEE computer graphics and applications 30, 3 (2010), 45--57. 1
Recommendations
Successive Lagrangian relaxation algorithm for nonconvex quadratic optimization
Optimization problems whose objective function and constraints are quadratic polynomials are called quadratically constrained quadratic programs (QCQPs). QCQPs are NP-hard in general and are important in optimization theory and practice. There have been ...
A Lagrangian---DNN relaxation: a fast method for computing tight lower bounds for a class of quadratic optimization problems
We propose an efficient computational method for linearly constrained quadratic optimization problems (QOPs) with complementarity constraints based on their Lagrangian and doubly nonnegative (DNN) relaxation and first-order algorithms. The simplified ...
Revisiting Lagrangian relaxation for network design
AbstractWe consider a general network design model for which we compare theoretically different Lagrangian relaxations. Fairly general assumptions on the model are proposed, allowing us to generalize results obtained for special cases. The ...
Comments
Please enable JavaScript to view thecomments powered by Disqus.Information & Contributors
Information
Published In
Publisher
Eurographics Association
Goslar, Germany
Publication History
Published: 04 June 2018
Qualifiers
- Research-article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 02 Oct 2024
Other Metrics
Citations
View Options
View options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in