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exercises:2015_pitt:ls

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exercises:2015_pitt:ls [2015/03/05 14:09] vondele |
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===== 1. Task: Scaling Behavior ===== | ===== 1. Task: Scaling Behavior ===== | ||

- | Calculate the energy of the 2D-polymer for various different system sizes, by using ''NREPX=1'', ''2'', ''3'', .... Perform each calculations with the linear scaling and the normal SCF method. Plot the time required for the last SCF cycle of each calculation vs. the system size. Extrapolate the time required for an SCF cycle of a system containing 10x10 unit cells. | + | Calculate the energy of the 2D-polymer for various different system sizes, by using ''NREPX=1'', ''2'', ''3'', .... Perform each calculation with the linear scaling and the normal SCF method. Plot the time required for the last SCF cycle of each calculation vs. the system size. Extrapolate the time required for an SCF cycle of a system containing 10x10 unit cells. |

The number of seconds required of each SCF cycle is printed as part of the regular output. | The number of seconds required of each SCF cycle is printed as part of the regular output. | ||

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===== 2. Task: Filter Threshold ===== | ===== 2. Task: Filter Threshold ===== | ||

- | Calculate the energy of the single unit-cell with the linear scaling method at different filter thresholds, by changing ''EPS_FILTER''. Plot the time required for the calculation and the obtained total energy vs the threshold. How does this compare with the total energy obtained from the normal SCF method? Note that this requires well converged SCF calculations (''EPS_SCF'') | + | Calculate the energy of the single unit-cell with the linear scaling method at different filter thresholds, by changing ''EPS_FILTER''. Plot the time required for the calculation and the obtained total energy vs the threshold. How does this compare with the total energy obtained from the normal SCF method? Note that this requires well converged SCF calculations (''EPS_SCF''). Also have a look at the sparsity report, which matrix is more dense (S or P) ? |

+ | | ||

+ | ===== 3. Task: LS algorithm ===== | ||

+ | | ||

+ | Finally, compare the efficiency of three different algorithms (using NREP 2x2). The following three options can be tried: | ||

+ | | ||

+ | sign matrix iterations [[doi>10.1021/ct200897x]] | ||

+ | <code> | ||

+ | ! linear scaling SCF | ||

+ | &LS_SCF | ||

+ | ! SIGN_MATRIX, only effective if the chemical potential is known in advance | ||

+ | PURIFICATION_METHOD SIGN_MATRIX | ||

+ | ! threshold used to determine sparsity and thus speed and accuracy | ||

+ | EPS_FILTER 1E-7 | ||

+ | ! convergence for the SCF | ||

+ | EPS_SCF 1E-5 | ||

+ | ! chemical potential, an energy from within in the HOMO-LUMO gap | ||

+ | MU -0.15 | ||

+ | S_PRECONDITIONER ATOMIC | ||

+ | &END | ||

+ | </code> | ||

+ | | ||

+ | trs4 iterations [[doi>10.1063/1.1559913]] | ||

+ | <code> | ||

+ | ! linear scaling SCF | ||

+ | &LS_SCF | ||

+ | ! TRS4, does not need an estimate for the chemical potential | ||

+ | PURIFICATION_METHOD TRS4 | ||

+ | ! threshold used to determine sparsity and thus speed and accuracy | ||

+ | EPS_FILTER 1E-7 | ||

+ | ! convergence for the SCF | ||

+ | EPS_SCF 1E-5 | ||

+ | ! chemical potential, an energy from within in the HOMO-LUMO gap | ||

+ | MU -0.15 | ||

+ | S_PRECONDITIONER ATOMIC | ||

+ | &END | ||

+ | </code> | ||

+ | | ||

+ | curvy steps [[doi>10.1063/1.1558476]] | ||

+ | <code> | ||

+ | ! linear scaling SCF | ||

+ | &LS_SCF | ||

+ | ! TRS4, does not need an estimate for the chemical potential | ||

+ | PURIFICATION_METHOD TRS4 | ||

+ | ! threshold used to determine sparsity and thus speed and accuracy | ||

+ | EPS_FILTER 1E-7 | ||

+ | ! convergence for the SCF | ||

+ | EPS_SCF 1E-5 | ||

+ | ! chemical potential, an energy from within in the HOMO-LUMO gap | ||

+ | MU -0.15 | ||

+ | S_PRECONDITIONER NONE | ||

+ | &CURVY_STEPS | ||

+ | &END CURVY_STEPS | ||

+ | &END | ||

+ | </code> | ||

+ | | ||

+ | In making your judgement, consider the fact that the rate of convergence might not be the same for all algorithms. | ||

+ | | ||

+ | From a practical point of view, the curvy_steps algorithm seems very robust in converging the SCF of electronically difficult systems, while the sign matrix algorithm is only worthwhile considering if the chemical potential is known (or fixed). | ||

===== Input File ===== | ===== Input File ===== |

exercises/2015_pitt/ls.txt · Last modified: 2015/03/05 15:04 by vondele

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