Analysis and visualization of complex vector fields remain major challenges when studying large scale simulation of physical phenomena. The primary reason is the gap between the concepts of smooth vector field theory and their computational realization. In practice, researchers must choose between either numerical techniques, with limited or no guarantees on how they preserve fundamental invariants, or discrete techniques which limit the precision at which the vector field can be represented. We propose a new representation of vector fields that combines the advantages of both approaches. In particular, we represent a subset of possible streamlines by storing their paths as they traverse the edges of a triangulation. Using only a finite set of streamlines creates a fully discrete version of a vector field that nevertheless approximates the smooth flow up to a user controlled error bound. The discrete nature of our representation enables us to directly compute and classify analogues of critical points, closed orbits, and other common topological structures. Further, by varying the number of divisions (quantizations) used per edge, we vary the resolution used to represent the field, allowing for controlled precision. This representation is compact in memory and supports standard vector field operations.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This work is supported in part by NSF awards IIS-1045032, OCI-0904631, OCI-0906379 and CCF-0702817, and by KAUST Award KUS-C1-016-04. This work was performed under the auspices of the U.S. DOE by the Univ. of Utah under contracts DE-SC0001922, DE-AC52-07NA27344, and DE-FC02-06ER25781, and LLNL under contract DE-AC52-07NA27344. We thank Guoning Chen, Eugene Zhang, and Andrzej Szymczak for helping us generate Fig. 9. We are grateful for data from Jackie Chen (Figs. 10 and 11(b)), Han-Wei Shen (Fig. 11(a)), and Mathew Maltrud from the Climate, Ocean and Sea Ice Modelling program at LANL and the BER Office of Science UV-CDAT team (Figs. 1, 5, 8, 9). LLNL-CONF-548652.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.