Figure 3

Mimetic discretizations of Maxwell’s equations (e.g. by FIT) use a primal and dual grid. The discrete temperatures $T_k$ are located at primary nodes, the line-integrated electric field and the magnetic vector potentials ${\stackrel{⏜}{e}}_k={\stackrel{⏜}{a}}_k^{\prime }$ are defined at primary edges and finally the facet-integrated source current density ${\stackrel{⏜}{\stackrel{⏜}{j}}}_k$ at dual surfaces. The material laws relate the quantities on both grids, e.g., the conductivity connects by Ohm’s Law the currents and voltages, i.e. ${\stackrel{⏜}{\stackrel{⏜}{j}}}_k={\sigma }_k(T_k){\stackrel{⏜}{e}}_k$. The figure shows the case for a current in x-direction.