{"paper":{"title":"A Comparison of Sparse Solvers for Severely Ill-Conditioned Linear Systems in Geophysical Marker-In-Cell Simulations","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Marcel Ferrari","submitted_at":"2024-09-17T19:38:43Z","abstract_excerpt":"Solving sparse linear systems is a critical challenge in many scientific and engineering fields, particularly when these systems are severely ill-conditioned. This work aims to provide a comprehensive comparison of various solvers designed for such problems, offering valuable insights and guidance for domain scientists and researchers. We develop the tools required to accurately evaluate the performance and correctness of 16 solvers from 11 state-of-the-art numerical libraries, focusing on their effectiveness in handling ill-conditioned matrices. The solvers were tested on linear systems arisi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.11515","kind":"arxiv","version":2},"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/2409.11515/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"}