Geometric algebra for vector fields analysis and visualization: mathematical settings, overview and applications

Chantal Oberson Ausoni (1) , Pascal Frey (2)

1 ISCD - Institut des Sciences du Calcul et des Données
2 LJLL - Laboratoire Jacques-Louis Lions

The formal language of Clifford's algebras is attracting an increasingly large community of mathematicians, physicists and software developers seduced by the conciseness and the efficiency of this compelling system of mathematics. This contribution will suggest how these concepts can be used to serve the purpose of scientific visualization and more specifically to reveal the general structure of complex vector fields. We will emphasize the elegance and the ubiquitous nature of the geometric algebra approach, as well as point out the computational issues at stake.

Keywords: vector field; topological structure; geometric algebra; visualization

Domains: Analysis of PDEs [math.AP]; Differential Geometry [math.DG]; Geometric Topology [math.GT]

Chantal Oberson Ausoni, Pascal Frey. Geometric algebra for vector fields analysis and visualization: mathematical settings, overview and applications. 2014. ⟨hal-00920544v2⟩