{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:HUYM3CDKQ7GI3DQZVG7HF732SQ","short_pith_number":"pith:HUYM3CDK","schema_version":"1.0","canonical_sha256":"3d30cd886a87cc8d8e19a9be72ff7a941dc6d44196a8bc5c52a7eb44a010a604","source":{"kind":"arxiv","id":"2408.08187","version":1},"attestation_state":"computed","paper":{"title":"A computational study of algebraic coarse spaces for two-level overlapping additive Schwarz preconditioners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Alexander Heinlein, Filipe A. C. S. Alves, Hadi Hajibeygi","submitted_at":"2024-08-15T14:44:37Z","abstract_excerpt":"The two-level overlapping additive Schwarz method offers a robust and scalable preconditioner for various linear systems resulting from elliptic problems. One of the key to these properties is the construction of the coarse space used to solve a global coupling problem, which traditionally requires information about the underlying discretization. An algebraic formulation of the coarse space reduces the complexity of its assembly. Furthermore, well-chosen coarse basis functions within this space can better represent changes in the problem's properties. Here we introduce an algebraic formulation"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2408.08187","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-08-15T14:44:37Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"f3d4b3a4c8a95617dda8685d31b587506971f1d11763381038b5f0823081512e","abstract_canon_sha256":"8162ea67d6da9dc067fe272fbf07d3444dd8b60030ddc0f9e601051e19f5024f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:55:45.705811Z","signature_b64":"efVuLu9VA4BZcHGrTa52FvvYgH2dzbTwnFw3LUaEQUmoYx6vKUY7DQmPXnM7iaFVDFqM+i2MF8f8Sx2IXc/MDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d30cd886a87cc8d8e19a9be72ff7a941dc6d44196a8bc5c52a7eb44a010a604","last_reissued_at":"2026-07-05T08:55:45.705295Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:55:45.705295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A computational study of algebraic coarse spaces for two-level overlapping additive Schwarz preconditioners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Alexander Heinlein, Filipe A. C. S. Alves, Hadi Hajibeygi","submitted_at":"2024-08-15T14:44:37Z","abstract_excerpt":"The two-level overlapping additive Schwarz method offers a robust and scalable preconditioner for various linear systems resulting from elliptic problems. One of the key to these properties is the construction of the coarse space used to solve a global coupling problem, which traditionally requires information about the underlying discretization. An algebraic formulation of the coarse space reduces the complexity of its assembly. Furthermore, well-chosen coarse basis functions within this space can better represent changes in the problem's properties. Here we introduce an algebraic formulation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.08187","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/2408.08187/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2408.08187","created_at":"2026-07-05T08:55:45.705367+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.08187v1","created_at":"2026-07-05T08:55:45.705367+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.08187","created_at":"2026-07-05T08:55:45.705367+00:00"},{"alias_kind":"pith_short_12","alias_value":"HUYM3CDKQ7GI","created_at":"2026-07-05T08:55:45.705367+00:00"},{"alias_kind":"pith_short_16","alias_value":"HUYM3CDKQ7GI3DQZ","created_at":"2026-07-05T08:55:45.705367+00:00"},{"alias_kind":"pith_short_8","alias_value":"HUYM3CDK","created_at":"2026-07-05T08:55:45.705367+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HUYM3CDKQ7GI3DQZVG7HF732SQ","json":"https://pith.science/pith/HUYM3CDKQ7GI3DQZVG7HF732SQ.json","graph_json":"https://pith.science/api/pith-number/HUYM3CDKQ7GI3DQZVG7HF732SQ/graph.json","events_json":"https://pith.science/api/pith-number/HUYM3CDKQ7GI3DQZVG7HF732SQ/events.json","paper":"https://pith.science/paper/HUYM3CDK"},"agent_actions":{"view_html":"https://pith.science/pith/HUYM3CDKQ7GI3DQZVG7HF732SQ","download_json":"https://pith.science/pith/HUYM3CDKQ7GI3DQZVG7HF732SQ.json","view_paper":"https://pith.science/paper/HUYM3CDK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.08187&json=true","fetch_graph":"https://pith.science/api/pith-number/HUYM3CDKQ7GI3DQZVG7HF732SQ/graph.json","fetch_events":"https://pith.science/api/pith-number/HUYM3CDKQ7GI3DQZVG7HF732SQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HUYM3CDKQ7GI3DQZVG7HF732SQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HUYM3CDKQ7GI3DQZVG7HF732SQ/action/storage_attestation","attest_author":"https://pith.science/pith/HUYM3CDKQ7GI3DQZVG7HF732SQ/action/author_attestation","sign_citation":"https://pith.science/pith/HUYM3CDKQ7GI3DQZVG7HF732SQ/action/citation_signature","submit_replication":"https://pith.science/pith/HUYM3CDKQ7GI3DQZVG7HF732SQ/action/replication_record"}},"created_at":"2026-07-05T08:55:45.705367+00:00","updated_at":"2026-07-05T08:55:45.705367+00:00"}