SPLINE DISCRETE DIFFERENTIAL FORMS AND A NEW FINITE DIFFERENCE DISCRETE HODGE OPERATOR

Aurore Back (1, 2) , Eric Sonnendrücker (3, 4)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - Ex E8 Dynamique non linéaire
3 CALVI - Scientific computation and visualization
4 IRMA - Institut de Recherche Mathématique Avancée

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: B-spline; discrete differential form; Maxwell equation; Hodge discretization

Domaines: Equations aux dérivées partielles [math.AP]

Aurore Back, Eric Sonnendrücker. SPLINE DISCRETE DIFFERENTIAL FORMS AND A NEW FINITE DIFFERENCE DISCRETE HODGE OPERATOR. 2014. ⟨hal-00822164v2⟩