A Fast Parallel Algorithm for Selected Inversion of Structured Sparse Matrices with Application to 2D Electronic Structure Calculations

Lin Lin, Chao Yang, Jianfeng Lu, Lexing Ying, Weinan E
2011 SIAM Journal on Scientific Computing  
An efficient parallel algorithm is presented and tested for computing selected components of H −1 where H has the structure of a Hamiltonian matrix of two-dimensional lattice models with local interaction. Calculations of this type are useful for several applications, including electronic structure analysis of materials in which the diagonal elements of the Green's functions are needed. The algorithm proposed here is a direct method based on an LDL T factorization. The elimination tree is used
more » ... o organize the parallel algorithm. Synchronization overhead is reduced by passing the data level by level along this tree using the technique of local buffers and relative indices. The performance of the proposed parallel algorithm is analyzed by examining its load balance and communication overhead, and is shown to exhibit an excellent weak scaling on a large-scale high performance parallel machine with distributed memory.
doi:10.1137/09077432x fatcat:6gt5l5eqojaxxmh56snnseh7ci