Spline discrete differential forms. Application to Maxwell' s equations.

Aurore Back (1) , Eric Sonnendrücker (1, 2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 CALVI - Scientific computation and visualization

We construct a new set of discrete differential forms based on B-splines of arbitrary degree as well as an associated Hodge operator. The theory is first developed in 1D and then extended to multi-dimension using tensor products. We link our discrete differential forms with the theory of chains and cochains. The spline discrete differential forms are then applied to the numerical solution of Maxwell's equations.

Mots clés: Discrete differential forms; B-splines; Maxwell; Numerical simulation

Domaines: Analyse numérique [math.NA]

Aurore Back, Eric Sonnendrücker. Spline discrete differential forms. Application to Maxwell' s equations.. 2011. ⟨hal-00568811⟩