## Charles HansenVolume RenderingRay Tracing Graphics |
## Valerio PascucciTopological MethodsData Streaming Big Data |
## Chris JohnsonVolume RenderingUncertainty Visualization |

## Mike KirbyUncertainty Visualization |
## Ross WhitakerTopological MethodsUncertainty Visualization |

- Modeling, Display, and Understanding Uncertainty in Simulations for Policy Decision Making
- NSF-OCI: A GPU-Enabled Toolbox for Solving Hamilton-Jacobi and Level Set Equations on Unstructured Meshes
- ViSUS: One billion polygons to billions of pixels
- Uncertainty Quantification and Visualization
- Analysis and Visualization of Stochastic Simulation Solutions
- NSF-CRI: A Hierarchical Data Storage System

Topological and Statistical Methods for Complex Data,Subtitled “Tackling Large-Scale, High-Dimensional, and Multivariate Data Spaces,” J. Bennett, F. Vivodtzev, V. Pascucci (Eds.).
Mathematics and Visualization, 2015. ISBN: 978-3-662-44899-1 This book contains papers presented at the Workshop on the Analysis of Large-scale, |

Overview and State-of-the-Art of Uncertainty VisualizationG.P. Bonneau, H.C. Hege, C.R. Johnson, M.M. Oliveira, K. Potter, P. Rheingans, T. Schultz. In Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization, Mathematics and Visualization, Ch. 1, Edited by M. Chen and H. Hagen and C.D. Hansen and C.R. Johnson and A. Kauffman, Springer-Verlag, pp. 3--27. 2014. ISBN: 978-1-4471-6496-8 ISSN: 1612-3786 DOI: 10.1007/978-1-4471-6497-5_1 The goal of visualization is to effectively and accurately communicate data. Visualization research has often overlooked the errors and uncertainty which accompany the scientific process and describe key characteristics used to fully understand the data. The lack of these representations can be attributed, in part, to the inherent difficulty in defining, characterizing, and controlling this uncertainty, and in part, to the difficulty in including additional visual metaphors in a well designed, potent display. However, the exclusion of this information cripples the use of visualization as a decision making tool due to the fact that the display is no longer a true representation of the data. This systematic omission of uncertainty commands fundamental research within the visualization community to address, integrate, and expect uncertainty information. In this chapter, we outline sources and models of uncertainty, give an overview of the state-of-the-art, provide general guidelines, outline small exemplary applications, and finally, discuss open problems in uncertainty visualization. |

In-situ feature extraction of large scale combustion simulations using segmented merge treesA.G. Landge, V. Pascucci, A. Gyulassy, J.C. Bennett, H. Kolla, J. Chen, P.-T. Bremer. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC 2014), New Orleans, Louisana, IEEE Press, Piscataway, NJ, USA pp. 1020--1031. 2014. ISBN: 978-1-4799-5500-8 DOI: 10.1109/SC.2014.88 The ever increasing amount of data generated by scientific simulations coupled with system I/O constraints are fueling a need for in-situ analysis techniques. Of particular interest are approaches that produce reduced data representations while maintaining the ability to redefine, extract, and study features in a post-process to obtain scientific insights. |

Efficient I/O and storage of adaptive-resolution dataS. Kumar, J. Edwards, P.-T. Bremer, A. Knoll, C. Christensen, V. Vishwanath, P. Carns, J.A. Schmidt, V. Pascucci. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, IEEE Press, pp. 413--423. 2014. DOI: 10.1109/SC.2014.39 We present an efficient, flexible, adaptive-resolution I/O framework that is suitable for both uniform and Adaptive Mesh Refinement (AMR) simulations. In an AMR setting, current solutions typically represent each resolution level as an independent grid which often results in inefficient storage and performance. Our technique coalesces domain data into a unified, multiresolution representation with fast, spatially aggregated I/O. Furthermore, our framework easily extends to importance-driven storage of uniform grids, for example, by storing regions of interest at full resolution and nonessential regions at lower resolution for visualization or analysis. Our framework, which is an extension of the PIDX framework, achieves state of the art disk usage and I/O performance regardless of resolution of the data, regions of interest, and the number of processes that generated the data. We demonstrate the scalability and efficiency of our framework using the Uintah and S3D large-scale combustion codes on the Mira and Edison supercomputers. |

Robust Detection of Singularities in Vector FieldsH. Bhatia, A. Gyulassy, H. Wang, P.-T. Bremer, V. Pascucci . In Topological Methods in Data Analysis and Visualization III, Mathematics and Visualization, Springer International Publishing, pp. 3--18. March, 2014. DOI: 10.1007/978-3-319-04099-8_1 Recent advances in computational science enable the creation of massive datasets of ever increasing resolution and complexity. Dealing effectively with such data requires new analysis techniques that are provably robust and that generate reproducible results on any machine. In this context, combinatorial methods become particularly attractive, as they are not sensitive to numerical instabilities or the details of a particular implementation. We introduce a robust method for detecting singularities in vector fields. We establish, in combinatorial terms, necessary and sufficient conditions for the existence of a critical point in a cell of a simplicial mesh for a large class of interpolation functions. These conditions are entirely local and lead to a provably consistent and practical algorithm to identify cells containing singularities. |

Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization,C.D. Hansen, M. Chen, C.R. Johnson, A.E. Kaufman, H. Hagen (Eds.). Mathematics and Visualization, Springer, 2014. ISBN: 978-1-4471-6496-8 |

Topological Methods in Data Analysis and Visualization IIIP.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert. Mathematics and Visualization, 2014. ISBN: 978-3-319-04099-8 |

The Natural Helmholtz-Hodge Decomposition For Open-Boundary Flow AnalysisH. Bhatia, V. Pascucci, P.-T. Bremer. In IEEE Transactions on Visualization and Computer Graphics (TVCG), Vol. 99, pp. 1566--1578. 2014. DOI: 10.1109/TVCG.2014.2312012 The Helmholtz-Hodge decomposition (HHD) describes a flow as the sum of an incompressible, an irrotational, and a harmonic flow, and is a fundamental tool for simulation and analysis. Unfortunately, for bounded domains, the HHD is not uniquely defined, and traditionally, boundary conditions are imposed to obtain a unique solution. However, in general, the boundary conditions used during the simulation may not be known and many simulations use open boundary conditions. In these cases, the flow imposed by traditional boundary conditions may not be compatible with the given data, which leads to sometimes drastic artifacts and distortions in all three components, hence producing unphysical results. Instead, this paper proposes the natural HHD, which is defined by separating the flow into internal and external components. Using a completely data-driven approach, the proposed technique obtains uniqueness without assuming boundary conditions a priori. As a result, it enables a reliable and artifact-free analysis for flows with open boundaries or unknown boundary conditions. Furthermore, our approach computes the HHD on a point-wise basis in contrast to the existing global techniques, and thus supports computing inexpensive local approximations for any subset of the domain. Finally, the technique is easy to implement for a variety of spatial discretizations and interpolated fields in both two and three dimensions. |

Extracting Features from Time-Dependent Vector Fields Using Internal Reference FramesH. Bhatia, V. Pascucci, R.M. Kirby, P.-T. Bremer. In Computer Graphics Forum, Vol. 33, No. 3, pp. 21--30. June, 2014. DOI: 10.1111/cgf.12358 Extracting features from complex, time-dependent flow fields remains a significant challenge despite substantial research efforts, especially because most flow features of interest are defined with respect to a given reference frame. Pathline-based techniques, such as the FTLE field, are complex to implement and resource intensive, whereas scalar transforms, such as λ |