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

Lin, L. ; Yang, C. ; Lu, J. ; Ying, L. ; Weinan, E.

Technical Information Center Oak Ridge Tennessee

关键词: Algorithms;    Sparse matrices;    Electronic structure;    Approximations;    Buffers;   

RP-ID  :  DE2010974182

学科分类：工程和技术（综合）

美国|英语

来源: National Technical Reports Library

【 摘 要 】

We present an efficient parallel algorithm and its implementation for computing the diagonal of H(-1) where H is a 2D Kohn-Sham Hamiltonian discretized on a rectangular domain using a standard order finite difference scheme. This type of calculation can be used to obtain an accurate approximation to the diagonal of a Fermi-Dirac function of H through a recently developed pole-second expansion technique. The diagonal elements are needed in electronic structure calculations for order quantum mechanical systems. We show how elimination tree is used to organize the parallel computation and how synchronization overhead is reduced by passing data level by level along this tree using the technique of local buffers and relative indices. We analyze the performance of our implementation by examining its load balance and communication overhead. We show that our implementation exhibits an excellent weak scaling on a large-scale high performance distributed parallel machine.