Compatible Discrete Operator (CDO) schemes are part of the mimetic discretization family. They are low-order schemes generalizing a number of classical schemes, e.g. Finite Elements, Finite Difference, Discrete Geometric Approach and the Covolume Method. These schemes are based on the decomposition of equations into two parts: a topological and a metric part. On the one hand, the topological relations are exactly discretized using the Stokes theorem for the curl operator. This leads to discrete equations that preserve the geometrical structure of Maxwell's equations. On the other hand, the material relations are discretized using material mass matrices which account for the duality between the fields using polynomial interpolations. For Maxwell's equations, the computational cost is concentrated in this metric part as the calculation of the electric field requires the inversion of a matrix. In this presentation we will discuss several strategies to make the scheme more efficient: metric design, meshes and schemes hybridization. The cornerstone of schemes hybridization lies in handling boundary conditions and to choose the ones that preserve the stability of the scheme. This will be detailed in a discussion about our recent works on the extension of the mimetic formalism proposed in to make explicit how to handle boundary conditions.