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Additionally, in order to further increase the capability of the algorithm in modeling particles of sizes comparable to the lattice spacing, we propose an improvement to the EI scheme, the complete equilibrium interpolation (CEI). This approach allows us to accurately capture the boundaries of the particle also when located between two fluid nodes. We evaluate the CEI performance in solving the dynamics of an under-resolved particle under analogous Stokes conditions and also for the case of a rotating ellipsoid in a shear flow. Finally, we show that EI and