Calculation of global quantities using incidence matrixes in the A-φ formulation

Inhalt:
To solve Maxwell's equations, different methods can be used such as Finite Element Method, Finite Integration Technique. In "Bossavit A., Kettunen L.,: Yee-likes schemes on taggered cellular-grids: a synthesis between FIT and FEM approaches", it has been shown that the previous methods can be obtained from a common scheme of discretisation based on the notion of dual meshes. Unknown fields are then vectors which components are fluxes flowing through facets or circulations along edges. Operators such as gradient, curl and divergence are replaced by incidence matrixes and the behaviour laws by matrix relations linked the vectors of the unknown fields. Recently, methods have been proposed to calculate or to impose global quantities such that magnetic fluxes, currents, ernfs or rnrnfs in FEM that satisfy conservation law and energy balance. In this communication, we propose to give the expression of such global quantities using the incidence matrixes in the case of A-φ formulation solved by the Finite Element Method.