Blocked-Davidson algorithm: Difference between revisions
Vaspmaster (talk | contribs) No edit summary |
Vaspmaster (talk | contribs) No edit summary |
||
Line 21: | Line 21: | ||
::<math>\{ \psi^d_k| k=1,..,n_1\} \Rightarrow \{ \psi_k| k=1,..,N_{\rm bands}\}</math>. | ::<math>\{ \psi^d_k| k=1,..,n_1\} \Rightarrow \{ \psi_k| k=1,..,N_{\rm bands}\}</math>. | ||
* Move on to the next block <math>\{ \psi^1_k| k=n_1+1,..,2 n_1\}</math>. | * Move on to the next block <math>\{ \psi^1_k| k=n_1+1,..,2 n_1\}</math>. | ||
* | * When {{TAG|LDIAG}}=.TRUE. (default), a Rayleigh-Ritz optimization in the complete subspace <math>\{ \psi_k| k=1,..,N_{\rm bands}\}</math> is performed after all orbitals have been optimized. | ||
The blocked-Davidson algorithm is approximately a factor of 1.5-2 slower than the [[RMM-DIIS]], but more robust. | The blocked-Davidson algorithm is approximately a factor of 1.5-2 slower than the [[RMM-DIIS]], but more robust. |
Revision as of 16:54, 13 November 2023
The workflow of the blocked-Davidson iterative matrix diagonalization scheme implemented in VASP is as follows:[1][2]
- Take a subset (block) of orbitals out of the total set of NBANDS orbitals:
- .
- Extend the subspace spanned by by adding the preconditioned residual vectors of :
- Rayleigh-Ritz optimization ("subspace rotation") within the -dimensional space spanned by , to determine the lowest eigenvectors:
- Extend the subspace with the residuals of :
- Rayleigh-Ritz optimization ("subspace rotation") within the -dimensional space spanned by :
- If need be the subspace may be extended by repetition of this cycle of adding residual vectors and Rayleigh-Ritz optimization of the resulting subspace:
- Per default VASP will not iterate deeper than , though it may break off even sooner when certain criteria that measure the convergence of the orbitals have been met.
- When the iteration is finished, store the optimized block of orbitals back into the set:
- .
- Move on to the next block .
- When LDIAG=.TRUE. (default), a Rayleigh-Ritz optimization in the complete subspace is performed after all orbitals have been optimized.
The blocked-Davidson algorithm is approximately a factor of 1.5-2 slower than the RMM-DIIS, but more robust.