{"paper":{"title":"A Distributed-memory Tridiagonal Solver Based on a Specialised Data Structure Optimised for CPU and GPU Architectures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"cs.DC","authors_text":"Paul Bartholomew, S\\'ebastien Lemaire, Semih Akkurt, Sylvain Laizet","submitted_at":"2024-11-20T18:31:39Z","abstract_excerpt":"Various numerical methods used for solving partial differential equations (PDE) result in tridiagonal systems. Solving tridiagonal systems on distributed-memory environments is not straightforward, and often requires significant amount of communication. In this article, we present a novel distributed-memory tridiagonal solver algorithm, DistD2-TDS, based on a specialised data structure. DistD2-TDS algorithm takes advantage of the diagonal dominance in tridiagonal systems to reduce the communications in distributed-memory environments. The underlying data structure plays a crucial role for the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13532","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.13532/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}