Performance of linear and cubic-scaling solvers based on modular implementation of the orbital minimization method in the SIESTA code

Performance of recently implemented linear and cubic-scaling solvers based on the orbital minimization method (OMM) in the SIESTA code is compared with the standard diagonalization approach. This modular implementation relies on the use of external libraries, such as MatrixSwitch, libOMM (both from Electronic Structure Library), DBCSR and ScaLAPACK, that efficiently deal with linear algebra and parallelization issues. Large-scale molecular dynamics simulations are carried out for a boron nitride layer as an example. It is shown that kinetic energy preconditioning or Cholesky factorization considerably improve performance of cubic-scaling OMM with dense matrices and it becomes faster than diagonalization. Using sparse matrices and localized wavefunctions, linear scaling with system size is achieved. For diagonalization and cubic-scaling OMM with kinetic energy preconditioning, the crossovers with linear-scaling methods are observed at about 700 and 1200 atoms, respectively. Good CPU scaling is observed for OMM with sparse matrices handled using the DBCSR library. The optimal block sizes for wavefunctions and basis functions in this case are around 10.

近期实施的基于轨道最小化方法（OMM）的线性与立方尺度求解器在SIESTA代码中的性能与标准对角化方法进行了比较。该模块化实现依赖于外部库的使用，如MatrixSwitch、libOMM（均来自电子结构库）、DBCSR和ScaLAPACK，这些库能够高效地处理线性代数和并行化问题。以氮化硼层为例，进行了大规模分子动力学模拟。研究表明，动能预条件或Cholesky分解显著提升了具有稠密矩阵的立方尺度OMM的性能，其速度甚至超过了对角化方法。通过使用稀疏矩阵和局域波函数，实现了与系统尺寸的线性缩放。对于具有动能预条件的对角化以及立方尺度OMM，分别在大约700和1200个原子时观察到与线性缩放方法的交叉点。使用处理稀疏矩阵的DBCSR库，OMM展现了良好的CPU缩放性能。在此情况下，波函数和基函数的最优块大小约为10。