Simulation of the energy analysis system of field-emission microdimensional matrix structures based on silicon carbide involves a multiscale distribution of the electric field over the emission centers - individual atoms on the surface of the emitter. The solution to the problem, due to the complex configuration of the computational domain, can only be obtained numerically. In a multiscale formulation, an approximate numerical solution is constructed using the finite element method on nested meshes in the COMSOL Multiphysics environment, with particular attention being paid to the conjugation of solutions on adjacent scales to transfer the boundary and initial conditions.