Propagator call counts for the two-level MGRIT cycle

For the literal operations of A declared two-level MGRIT coarse-correction cycle, put $N_f=N$ and $N_c=N\mathrm{/}m$. One F-relaxation uses $N_f-N_c-1$ fine-propagator calls; one C-relaxation uses $N_c$; and one FCF-relaxation uses $2(N_f-N_c-1)+N_c$. The specified coarse forward substitution uses $N_c$ practical coarse-propagator applications, including the evaluation at $z_0=0$. These counts concern completed operations without eliminating calls at zero inputs.

In an additive accounting model with nonnegative call costs $c_{\mathrm{\Phi }},c_{\mathrm{\Psi }}$, the modeled work is $n_{\mathrm{\Phi }}{c}_{\mathrm{\Phi }}+n_{\mathrm{\Psi }}{c}_{\mathrm{\Psi }}+\kappa$, where $n_{\mathrm{\Phi }},n_{\mathrm{\Psi }}$ count all executed calls and $\kappa$ accounts for all remaining work. Residuals, restriction, interpolation and stopping checks must contribute their actual calls and overhead; cached values incur no new call. A parallel schedule must respect the serial order within each F-interval and in the coarse solve, and its communication and synchronization. No measured speedup is asserted.