We consider temporally evolving trees with changing topology and data: tree nodes may persist for a time range, merge or split, and the associated data may change. Essentially, one can think of this as a time series of trees with a node correspondence per hierarchy level between consecutive time steps. Existing visualization approaches for such data include animated 2D treemaps, where the dynamically changing layout makes it difficult to observe the data in its entirety. We present a method to visualize this dynamic data in a static, nested, and space-filling visualization. This is based on two major contributions: First, the layout constitutes a graph drawing problem. We approach it for the entire time span at once using a combination of a heuristic and simulated annealing. Second, we propose a rendering that emphasizes the hierarchy through an adaption of the classic cushion treemaps. We showcase the wide range of applicability using data from feature tracking in time-dependent scalar fields, evolution of file system hierarchies, and world population.

Percolation analysis is a valuable tool to study the statistical properties of turbulent flows. It is based on computing the percolation function for a derived scalar field, thereby quantifying the relative volume of the largest connected component in a superlevel set for a decreasing threshold. We propose a novel memory-distributed parallel algorithm to finely sample the percolation function. It is based on a parallel version of the union-find algorithm interleaved with a global synchronization step for each threshold sample. The efficiency of this algorithm stems from the fact that operations inbetween threshold samples can be freely reordered, are mostly local and thus require no inter-process communication. Our algorithm is significantly faster than previous algorithms for this purpose, and is neither constrained by memory size nor number of compute nodes compared to the conceptually related algorithm for extracting augmented merge trees. This makes percolation analysis much more accessible in a large range of scenarios. We explore the scaling of our algorithm for different data sizes, number of samples and number of MPI processes. We demonstrate the utility of percolation analysis using large turbulent flow data sets.

Percolation analysis is used to explore the connectivity of randomly connected infinite graphs. In the finite case, a closely related percolation function captures the relative volume of the largest connected component in a scalar field's superlevel set. While prior work has shown that random scalar fields with little spatial correlation yield a sharp transition in this function, little is known about its behavior on real data. In this work, we explore how different characteristics of a scalar field -such as its histogram or degree of structure -influence the shape of the percolation function. We estimate the critical value and transition width of the percolation function, and propose a corresponding normalization scheme that relates these values to known results on infinite graphs. In our experiments, we find that percolation analysis can be used to analyze the degree of structure in Gaussian random fields. On a simulated turbulent duct flow data set we observe that the critical values are stable and consistent across time. Our normalization scheme indeed aids comparison between data sets and relation to infinite graphs.

In situ visualization on high-performance computing systems allows us to analyze simulation results that would otherwise be impossible, given the size of the simulation data sets and offline post-processing execution time. We develop an in situ adaptor for Paraview Catalyst and Nek5000, a massively parallel Fortran and C code for computational fluid dynamics. We perform a strong scalability test up to 2048 cores on KTH’s Beskow Cray XC40 supercomputer and assess in situ visualization’s impact on the Nek5000 performance. In our study case, a high-fidelity simulation of turbulent flow, we observe that in situ operations significantly limit the strong scalability of the code, reducing the relative parallel efficiency to only $$\approx 21\%$$ ≈ 21 % on 2048 cores (the relative efficiency of Nek5000 without in situ operations is $$\approx 99\%$$ ≈ 99 % ). Through profiling with Arm MAP, we identified a bottleneck in the image composition step (that uses the Radix-kr algorithm) where a majority of the time is spent on MPI communication. We also identified an imbalance of in situ processing time between rank 0 and all other ranks. In our case, better scaling and load-balancing in the parallel image composition would considerably improve the performance of Nek5000 with in situ capabilities. In general, the result of this study highlights the technical challenges posed by the integration of high-performance simulation codes and data-analysis libraries and their practical use in complex cases, even when efficient algorithms already exist for a certain application scenario.

strong storm over Scandinavia strong storm over the British Isles and Norway cyclone Lothar cyclone Martin -35 0 35 sea level pressure anomaly [hPa] linearized space linearized space Figure 1. A temporal merge tree map (top) is a static visualization of a time-dependent scalar field (bottom). Our method uses augmented merge trees to map the data samples of each time step to a vertical slice. An optimization scheme is employed to achieve a temporally coherent mapping. The shown Storms data set represents storm activity over Europe in December 1999 and contains 744 time steps, arranged from left to right. Cyclones can easily be identified as dark blue lines and compared with each other wrt. their strength, lifetime, and footprint, while still being shown in the context of the entire data. Temporal merge tree maps can serve as data analysis tools in their own right, or be used to augment animations and other views. With some parallel processing, the above image can be computed in less than 15 seconds.