We present the Feature Tracking Kit (FTK), a framework that simplifies, scales, and delivers various feature-tracking algorithms for scientific data. The key of FTK is our simplicial spacetime meshing scheme that generalizes both regular and unstructured spatial meshes to spacetime while tessellating spacetime mesh elements into simplices. The benefits of using simplicial spacetime meshes include (1) reducing ambiguity cases for feature extraction and tracking, (2) simplifying the handling of degeneracies using symbolic perturbations, and (3) enabling scalable and parallel processing. The use of simplicial spacetime meshing simplifies and improves the implementation of several feature-tracking algorithms for critical points, quantum vortices, and isosurfaces. As a software framework, FTK provides end users with VTK/ParaView filters, Python bindings, a command line interface, and programming interfaces for feature-tracking applications. We demonstrate use cases as well as scalability studies through both synthetic data and scientific applications including tokamak, fluid dynamics, and superconductivity simulations. We also conduct end-to-end performance studies on the Summit supercomputer. FTK is open sourced under the MIT license: https://github.com/hguo/ftk.

We investigate the representation of discrete scientific data with a Ckfunctional model, where Ckdenotes k-th order continuity, in a distributed-memory parallel setting. The Multivariate Functional Approximation (MFA) model is a piecewise-continuous functional approximation based on multi-variate high-dimensional B-splines. When computing an MFA approximation in parallel over multiple blocks in a spatial domain decomposition, the interior of each block will be Ck, k being the B-spline polynomial degree, but discontinuities exist across neighboring block boundaries. We present an efficient and scalable solution that involves blending neighboring approximations to ensure Ckcontinuity across block boundaries. We show that after decomposing the domain in structured, overlapping blocks and approximating blocks independently to high degrees of accuracy, we can extend the local solution, in a postprocessing step, to the global domain by using compact, multidimensional smoothstep functions. We prove that this approach, which can be viewed as an extended partition of unity approximation method, is scalable on high-performance computing architectures.