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    Area of Science:

    • Computational topology
    • Data analysis and visualization
    • Scientific computing

    Background:

    • Topological techniques, particularly Morse-Smale complexes, are vital for analyzing large-scale scientific data.
    • Existing parallel methods for computing Morse-Smale complexes introduce geometric artifacts due to their discrete nature.

    Purpose of the Study:

    • To develop a new approach for constructing high-quality discrete Morse-Smale complexes.
    • To address the limitations of existing methods by reducing grid artifacts and improving geometric accuracy.
    • To enable the analysis of larger datasets with improved computational efficiency.

    Main Methods:

    • Combines parallel streamline computation with combinatorial methods.
    • Constructs discrete Morse-Smale complexes invariant to grid orientation.
    • Allows selective reconstruction of ascending/descending manifolds for focused analysis.

    Main Results:

    • Achieves high-quality discrete Morse-Smale complexes with reduced geometric artifacts.
    • Demonstrates improved computational performance, enabling analysis of larger datasets.
    • Validated across diverse scientific domains, showcasing broad applicability.

    Conclusions:

    • The presented approach offers a significant advancement in computing Morse-Smale complexes for large-scale data.
    • It provides a robust framework for feature definition and computation with enhanced geometric accuracy.
    • This method facilitates more efficient and reliable scientific data analysis.