Scientific simulations and experiments are producing increasingly large so-called multifield datasets that are comprised of scalar, vector, and tensor fields tracked over time. The visualization literature provides a variety of surface-based feature characterizations. While these models have proven extremely valuable in the analysis of individual fields, their use in practice is hindered by two major challenges.

First, the extraction of these structures is often non-trivial as their precise computation requires careful analysis of the spatial variation of convoluted functions and their nonlinear invariants. Examples of such characterizations include so-called crease surfaces and level sets in nonlinear fields. In addition, these surfaces can be non-orientable, with a nontrivial topology, and a complex set of boundaries. To address these issues we have introduced a novel scalable front propagation strategy that offers strong guarantees on the approximation quality. Our solution is suitable for arbitrarily complex surfaces, and it ensures an excellent geometric quality for the produced mesh.

A second, and arguably more severe limitation of these structure definitions is that they do not support the visual analysis of multifield datasets. In that context, we have proposed a geometrically motivated, multifield feature definition that characterizes the relationship between the features exhibited by the individual fields in the spatial domain of the problem. Our algorithm leverages the existing theory of skeleton derivation to simplify and fuse the surface structures from the constitutive fields into a coherent and visually effective data description. This work also introduced a new method for non-rigid surface registration tailored to the specific nature of surfaces extracted from computational fluid dynamics datasets. Temporal matching and spatial clustering enable the discovery of subtle interaction patterns between the different fields and their evolution over time.

Finally, we document the unified visual analysis achieved by our methods in the context of several multifield problems from large-scale time-varying simulations, and we discuss future research directions.