Fig 13. Visualization of the final matrix structure.

Using the hybrid approach, we can compute blood flow by solving a single linear system, assembled from the equations describing the finite volume discretization in the continuum (FV, in green), the network approach in the arteriolar and venular trees (AV, in black) and the coupling model at the interface of the two frameworks (coupling, in red). This yields a sparse matrix that is schematized here. Plain lines and dots represent non-zero values. The components (P_i)_i, (π_α)_α and (π_s)_s are the unknowns of the linear system, corresponding to FV, AV and coupling parts, respectively.