Convergence of dielectric constant with respect the number of k-points can be very slow in many systems. For this reason in Lumen it is implemented a double-grid technique that speeds up convergence versus k-points with a computational cost comparable to the standard calculations.
Here we provide a tutorial for this approach:
https://www.lumen-code.org/wiki/index.php?title=Fast_convergence_of_dielectric_constant_with_double_grid
The method for the Haydock solver is described in this paper:
Double k-Grid Method for Solving the Bethe-Salpeter Equation via Lanczos Approaches ,I.M. Alliati, D. Sangalli, M. Gruning, Frontiers in Chemistry, 9, p.763946 (2022)
while the old one that uses the inversion solver is described here:
Speeding up the solution of the Bethe-Salpeter equation by a double-grid method and Wannier interpolation, D. Kammerlander, S. Botti,M. A. L Marques, A. Marini and C. Attaccalite, Phys. Rev. B 86 (2012)
