高效率的大规模并行求解广义本征值方程是在计算电子结构等高性能计算学科中的一个重要课题,在未来E级计算的发展上有重要的意义。根据马普研究所近几年开发的一种面向P级应用的本征值求解库(eigenvalue solver for petaflop-applicatio...高效率的大规模并行求解广义本征值方程是在计算电子结构等高性能计算学科中的一个重要课题,在未来E级计算的发展上有重要的意义。根据马普研究所近几年开发的一种面向P级应用的本征值求解库(eigenvalue solver for petaflop-applications,ELPA),针对广义本征值问题,开发了一款开源并行广义本征值求解器Gen ELPA,实现了从广义本征值问题到一般本征值问题的转换方法,避免了潜在的问题;然后调用ELPA进行计算,具有良好的计算速度和并行效率;同时采用了类似Sca LAPACK的接口,更加易于使用。在第一性原理软件ABACUS(atomic-orbital based ab-initio computation at USTC)中的实际应用表明该求解器具有理想的计算速度提升。展开更多
The effective mass one-dimensional Schroedinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. T...The effective mass one-dimensional Schroedinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.展开更多
We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formal- ism of the Dirac equation with a generalized Hylleraas potential of the form V（τ）= V0（a ＋ exp （λτ））/（b ...We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formal- ism of the Dirac equation with a generalized Hylleraas potential of the form V（τ）= V0（a ＋ exp （λτ））/（b ＋ exp （λτ）） ＋ V1（ d ＋ exp （ λτ） ） / （b ＋ exp （λτ））. We obtain the bound state energy eigenvalue and the corresponding eigenfunction ex- pressed in terms of the Jaeobi polynomials. By choosing appropriate parameter in the potential model, the generalized Hylleraas potential reduces to the well known potentials as special cases.展开更多
文摘高效率的大规模并行求解广义本征值方程是在计算电子结构等高性能计算学科中的一个重要课题,在未来E级计算的发展上有重要的意义。根据马普研究所近几年开发的一种面向P级应用的本征值求解库(eigenvalue solver for petaflop-applications,ELPA),针对广义本征值问题,开发了一款开源并行广义本征值求解器Gen ELPA,实现了从广义本征值问题到一般本征值问题的转换方法,避免了潜在的问题;然后调用ELPA进行计算,具有良好的计算速度和并行效率;同时采用了类似Sca LAPACK的接口,更加易于使用。在第一性原理软件ABACUS(atomic-orbital based ab-initio computation at USTC)中的实际应用表明该求解器具有理想的计算速度提升。
文摘The effective mass one-dimensional Schroedinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.
文摘We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formal- ism of the Dirac equation with a generalized Hylleraas potential of the form V（τ）= V0（a ＋ exp （λτ））/（b ＋ exp （λτ）） ＋ V1（ d ＋ exp （ λτ） ） / （b ＋ exp （λτ））. We obtain the bound state energy eigenvalue and the corresponding eigenfunction ex- pressed in terms of the Jaeobi polynomials. By choosing appropriate parameter in the potential model, the generalized Hylleraas potential reduces to the well known potentials as special cases.
