More robust Chebyshev filtering for SCF iteration, with applications in real-space DFT

Chebyshev filtered subspace iteration (CheFSI) is a popular and powerful solver for the eigenvalue problems embedded in electronic structure calculations. Effective use of ChFSI requires that the user choose good values for several parameters, notably the filter degree d. Finding a good value for d is typically done with user experience and some trial and error. If the user chooses a bad value for d, then convergence can be slow. For real-space computation using high-accuracy discretizations, the degree search space may be exceptionally large, making the search for a good degree difficult. We develop a method that is more robust to the consequences of bad choices of d; we also provide a heuristic-based method for choosing d automatically if the user is not able to venture a good guess. We note that only by-products of CheFSI are needed to track filter performance. We provide examples that demonstrate near-equivalence to CheFSI when d is near-optimal, and a reduction in computational resource requirements in other cases.