PSelInv – A distributed memory parallel algorithm for selected inversion: The non-symmetric case

Journal Article · Tue May 01 00:00:00 EDT 2018 · Parallel Computing

DOI:https://doi.org/10.1016/j.parco.2017.11.009· OSTI ID:1478750

Jacquelin, Mathias ^[1]; Lin, Lin ^[2]; Yang, Chao ^[1]

---

1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.
2. Univ. of California, Berkeley, CA (United States). Dept. of Mathematics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.

This paper generalizes the parallel selected inversion algorithm called PSelInv to sparse non-symmetric matrices. We assume a general sparse matrix A has been decomposed as on a distributed memory parallel machine, where L, U are lower and upper triangular matrices, and P, Q are permutation matrices, respectively. The PSelInv method computes selected elements of . The selection is confined by the sparsity pattern of the matrix AT. Our algorithm does not assume any symmetry properties of A, and our parallel implementation is memory efficient, in the sense that the computed elements of overwrites the sparse matrix in situ. PSelInv involves a large number of collective data communication activities within different processor groups of various sizes. In order to minimize idle time and improve load balancing, tree-based asynchronous communication is used to coordinate all such collective communication. Numerical results demonstrate that PSelInv can scale efficiently to 6,400 cores for a variety of matrices

• Research Organization: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES)
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 1478750
• Journal Information: Parallel Computing, Vol. 74, Issue C; ISSN 0167-8191
• Country of Publication: United States
• Language: English