24 research outputs found
Efficient computation of the second-Born self-energy using tensor-contraction operations
In the nonequilibrium Green's function approach, the approximation of the
correlation self-energy at the second-Born level is of particular interest,
since it allows for a maximal speed-up in computational scaling when used
together with the Generalized Kadanoff-Baym Ansatz for the Green's function.
The present day numerical time-propagation algorithms for the Green's function
are able to tackle first principles simulations of atoms and molecules, but
they are limited to relatively small systems due to unfavourable scaling of
self-energy diagrams with respect to the basis size. We propose an efficient
computation of the self-energy diagrams by using tensor-contraction operations
to transform the internal summations into functions of external low-level
linear algebra libraries. We discuss the achieved computational speed-up in
transient electron dynamics in selected molecular systems.Comment: 9 pages, 4 figures, 1 tabl
Scalable Task-Based Algorithm for Multiplication of Block-Rank-Sparse Matrices
A task-based formulation of Scalable Universal Matrix Multiplication
Algorithm (SUMMA), a popular algorithm for matrix multiplication (MM), is
applied to the multiplication of hierarchy-free, rank-structured matrices that
appear in the domain of quantum chemistry (QC). The novel features of our
formulation are: (1) concurrent scheduling of multiple SUMMA iterations, and
(2) fine-grained task-based composition. These features make it tolerant of the
load imbalance due to the irregular matrix structure and eliminate all
artifactual sources of global synchronization.Scalability of iterative
computation of square-root inverse of block-rank-sparse QC matrices is
demonstrated; for full-rank (dense) matrices the performance of our SUMMA
formulation usually exceeds that of the state-of-the-art dense MM
implementations (ScaLAPACK and Cyclops Tensor Framework).Comment: 8 pages, 6 figures, accepted to IA3 2015. arXiv admin note: text
overlap with arXiv:1504.0504