Advection-Based Sparse Data Management for Visualizing Unsteady Flow

SmartCube: An Adaptive Data Management Architecture for the Real-Time Visualization of Spatiotemporal Datasets

Interactive visualization and exploration of large spatiotemporal data sets is difficult without carefully-designed data pre-processing and management tools. We propose a novel architecture for spatiotemporal data management. The architecture can dynamically update itself based on user queries. Datasets is stored in a tree-like structure to support memory sharing among cuboids in a logical structure of data cubes. An update mechanism is designed to create or remove cuboids on it, according to the analysis of the user queries, with the consideration of memory size limitation. Data structure is dynamically optimized according to different user queries. During a query process, user queries are recorded to predict the performance increment of the new cuboid. The creation or deletion of a cuboid is determined by performance increment. Experiment results show that our prototype system deliveries good performance towards user queries on different spatiotemporal datasets, which costing small memory size with comparable performance compared with other state-of-the-art algorithms.

Extreme-Scale Stochastic Particle Tracing for Uncertain Unsteady Flow Visualization and Analysis

We present an efficient and scalable solution to estimate uncertain transport behaviors-stochastic flow maps (SFMs)-for visualizing and analyzing uncertain unsteady flows. Computing flow maps from uncertain flow fields is extremely expensive because it requires many Monte Carlo runs to trace densely seeded particles in the flow. We reduce the computational cost by decoupling the time dependencies in SFMs so that we can process shorter sub time intervals independently and then compose them together for longer time periods. Adaptive refinement is also used to reduce the number of runs for each location. We parallelize over tasks-packets of particles in our design-to achieve high efficiency in MPI/thread hybrid programming. Such a task model also enables CPU/GPU coprocessing. We show the scalability on two supercomputers, Mira (up to 256K Blue Gene/Q cores) and Titan (up to 128K Opteron cores and 8K GPUs), that can trace billions of particles in seconds.

Finite-Time Lyapunov Exponents and Lagrangian Coherent Structures in Uncertain Unsteady Flows

The objective of this paper is to understand transport behavior in uncertain time-varying flow fields by redefining the finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structure (LCS) as stochastic counterparts of their traditional deterministic definitions. Three new concepts are introduced: the distribution of the FTLE (D-FTLE), the FTLE of distributions (FTLE-D), and uncertain LCS (U-LCS). The D-FTLE is the probability density function of FTLE values for every spatiotemporal location, which can be visualized with different statistical measurements. The FTLE-D extends the deterministic FTLE by measuring the divergence of particle distributions. It gives a statistical overview of how transport behaviors vary in neighborhood locations. The U-LCS, the probabilities of finding LCSs over the domain, can be extracted with stochastic ridge finding and density estimation algorithms. We show that our approach produces better results than existing variance-based methods do. Our experiments also show that the combination of D-FTLE, FTLE-D, and U-LCS can help users understand transport behaviors and find separatrices in ensemble simulations of atmospheric processes.