{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WE2XDACUPGJYARYGJSGWBSYNOP","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":"eb7e7ac72dc42509e94eee704f5753cbd89a58be2539fa58d85e3e9fb2adb393","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-26T16:06:44Z","title_canon_sha256":"4b7226f37e03af3901ba8f8fe694abcfe67366a8e611bc7c1a4cb27ad1695aec"},"schema_version":"1.0","source":{"id":"1903.10977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.10977","created_at":"2026-06-04T20:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1903.10977v1","created_at":"2026-06-04T20:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10977","created_at":"2026-06-04T20:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"WE2XDACUPGJY","created_at":"2026-06-04T20:14:17Z"},{"alias_kind":"pith_short_16","alias_value":"WE2XDACUPGJYARYG","created_at":"2026-06-04T20:14:17Z"},{"alias_kind":"pith_short_8","alias_value":"WE2XDACU","created_at":"2026-06-04T20:14:17Z"}],"graph_snapshots":[{"event_id":"sha256:af4a3c9ffa643664e6dc4683afad74d1b794172749f8f2590e92db5c7a3f706d","target":"graph","created_at":"2026-06-04T20:14:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1903.10977/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Ill-conditioning of the system matrix is a well-known complication in immersed finite element methods and trimmed isogeometric analysis. Elements with small intersections with the physical domain yield problematic eigenvalues in the system matrix, which generally degrades efficiency and robustness of iterative solvers. In this contribution we investigate the spectral properties of immersed finite element systems treated by Schwarz-type methods, to establish the suitability of these as smoothers in a multigrid method. Based on this investigation we develop a geometric multigrid preconditioner f","authors_text":"C. Messe, C.V. Verhoosel, E.H. van Brummelen, F. de Prenter, J.A. Evans, J. Benzaken, K. Maute","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-26T16:06:44Z","title":"Scalable multigrid methods for immersed finite element methods and immersed isogeometric analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10977","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":"sha256:0d6d8312299b23cb2618a87fb647f4e30e550595bbfad8cac21b1dc3570d962b","target":"record","created_at":"2026-06-04T20:14:17Z","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":"eb7e7ac72dc42509e94eee704f5753cbd89a58be2539fa58d85e3e9fb2adb393","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-26T16:06:44Z","title_canon_sha256":"4b7226f37e03af3901ba8f8fe694abcfe67366a8e611bc7c1a4cb27ad1695aec"},"schema_version":"1.0","source":{"id":"1903.10977","kind":"arxiv","version":1}},"canonical_sha256":"b13571805479938047064c8d60cb0d73c218bb76fa89194ee7f27a4cffb5245f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b13571805479938047064c8d60cb0d73c218bb76fa89194ee7f27a4cffb5245f","first_computed_at":"2026-06-04T20:14:17.895898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T20:14:17.895898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Xz66Ddy1VroCJlO1YsVSM5liCPlSWIc1gpm+uD+I7a3kKSjE9BKsc2E6gmsXBvwG/rVcLtA4JySVTyQGRFhBQ==","signature_status":"signed_v1","signed_at":"2026-06-04T20:14:17.896392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.10977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d6d8312299b23cb2618a87fb647f4e30e550595bbfad8cac21b1dc3570d962b","sha256:af4a3c9ffa643664e6dc4683afad74d1b794172749f8f2590e92db5c7a3f706d"],"state_sha256":"4425f90bd7b5f7c324493a8f7abcf3e5f81aa92959fbd745592fed9aa786b46d"}