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Math. Softw."],"published-print":{"date-parts":[[2017,9,30]]},"abstract":"<jats:p>\n                    We describe an efficient parallel implementation of the selected inversion algorithm for distributed memory computer systems, which we call PSelInv. The PSelInv method computes selected elements of a general sparse matrix\n                    <jats:italic toggle=\"yes\">A<\/jats:italic>\n                    that can be decomposed as\n                    <jats:italic toggle=\"yes\">A<\/jats:italic>\n                    =\n                    <jats:italic toggle=\"yes\">LU<\/jats:italic>\n                    , where\n                    <jats:italic toggle=\"yes\">L<\/jats:italic>\n                    is lower triangular and\n                    <jats:italic toggle=\"yes\">U<\/jats:italic>\n                    is upper triangular. The implementation described in this article focuses on the case of sparse symmetric matrices. It contains an interface that is compatible with the distributed memory parallel sparse direct factorization SuperLU_DIST. However, the underlying data structure and design of PSelInv allows it to be easily combined with other factorization routines, such as PARDISO. We discuss general parallelization strategies such as data and task distribution schemes. In particular, we describe how to exploit the concurrency exposed by the elimination tree associated with the\n                    <jats:italic toggle=\"yes\">LU<\/jats:italic>\n                    factorization of\n                    <jats:italic toggle=\"yes\">A<\/jats:italic>\n                    . We demonstrate the efficiency and accuracy of PSelInv by presenting several numerical experiments. In particular, we show that PSelInv can run efficiently on more than 4,000 cores for a modestly sized matrix. We also demonstrate how PSelInv can be used to accelerate large-scale electronic structure calculations.\n                  <\/jats:p>","DOI":"10.1145\/2786977","type":"journal-article","created":{"date-parts":[[2016,12,21]],"date-time":"2016-12-21T09:45:06Z","timestamp":1482313506000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":12,"title":["PSelInv\u2014A Distributed Memory Parallel Algorithm for Selected Inversion"],"prefix":"10.1145","volume":"43","author":[{"given":"Mathias","family":"Jacquelin","sequence":"first","affiliation":[{"name":"Lawrence Berkeley National Laboratory, Berkeley CA USA"}]},{"given":"Lin","family":"Lin","sequence":"additional","affiliation":[{"name":"University of California, Berkeley and Lawrence Berkeley National Laboratory, Berkeley CA"}]},{"given":"Chao","family":"Yang","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Laboratory, Berkeley CA USA"}]}],"member":"320","published-online":{"date-parts":[[2016,12,21]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899358194"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/100799411"},{"key":"e_1_2_1_3_1","unstructured":"P. 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