{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:36MJLERW2YKFP66DJB2X2GV2OW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cc15880c8592bb3ade478194a0557bc34c6b13292469ab976d6ea15c86d58bdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-08-29T14:35:27Z","title_canon_sha256":"5cdea9b277bedfdd7168a6741ebe00bccc109367c06e844385bf8705ce1dd2b4"},"schema_version":"1.0","source":{"id":"1708.08782","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08782","created_at":"2026-05-18T00:36:25Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08782v1","created_at":"2026-05-18T00:36:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08782","created_at":"2026-05-18T00:36:25Z"},{"alias_kind":"pith_short_12","alias_value":"36MJLERW2YKF","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"36MJLERW2YKFP66D","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"36MJLERW","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:a34499679205c91750009a1e24601c07cae81ef63d5d938e00f51b319a7fb3ac","target":"graph","created_at":"2026-05-18T00:36:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we aim at solving the Biot model under stabilized finite element discretizations. To solve the resulting generalized saddle point linear systems, some iterative methods are proposed and compared. In the first method, we apply the GMRES algorithm as the outer iteration. In the second method, the Uzawa method with variable relaxation parameters is employed as the outer iteration method. In the third approach, Uzawa method is treated as a fixed-point iteration, the outer solver is the so-called Anderson acceleration. In all these methods, the inner solvers are preconditioners for t","authors_text":"Guoping Zhang, Mingchao Cai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-08-29T14:35:27Z","title":"Comparisons of Some Iterative Algorithms for Biot Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08782","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:096735b1cd9fd5f441bd22a1874aca1768293abf44c54f7ccdae28da9a1df775","target":"record","created_at":"2026-05-18T00:36:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cc15880c8592bb3ade478194a0557bc34c6b13292469ab976d6ea15c86d58bdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-08-29T14:35:27Z","title_canon_sha256":"5cdea9b277bedfdd7168a6741ebe00bccc109367c06e844385bf8705ce1dd2b4"},"schema_version":"1.0","source":{"id":"1708.08782","kind":"arxiv","version":1}},"canonical_sha256":"df98959236d61457fbc348757d1aba75bc427d4a84f35213e08538c8d4eab057","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df98959236d61457fbc348757d1aba75bc427d4a84f35213e08538c8d4eab057","first_computed_at":"2026-05-18T00:36:25.666729Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:25.666729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c7rec0q/EMKoZ4WZunkJ8XrevnE9ayeSbaG5+I7fqwU69NNIRT/pTJCCxqA88enE+TGSVFlRNCMMW2p84t9vAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:25.667430Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.08782","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:096735b1cd9fd5f441bd22a1874aca1768293abf44c54f7ccdae28da9a1df775","sha256:a34499679205c91750009a1e24601c07cae81ef63d5d938e00f51b319a7fb3ac"],"state_sha256":"6d3ea9f2c77fec7b78fcbfcc9f673533179cc813072edb26f62ed532b68ac6eb"}