{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:77CBG24ZDUK7ZH35QJQ7S3LVFD","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":"8a843a11faf3ee563b460ed4ee7a46561e2943a6835169ddf6a061f28f66076f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-19T21:08:07Z","title_canon_sha256":"8966be0349fcef40c93857e1311cf3a4dc99ce04a63d0f89a92e1182546ce965"},"schema_version":"1.0","source":{"id":"1908.07071","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07071","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07071v2","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07071","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"77CBG24ZDUK7","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_16","alias_value":"77CBG24ZDUK7ZH35","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_8","alias_value":"77CBG24Z","created_at":"2026-07-05T02:21:49Z"}],"graph_snapshots":[{"event_id":"sha256:d45179c30df02e5a164c496e26b9a52836ddcf4f14a0a53dadd4e97a8263f56a","target":"graph","created_at":"2026-07-05T02:21:49Z","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/1908.07071/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we design preconditioners for the matrix-free solution of high-order continuous and discontinuous Galerkin discretizations of elliptic problems based on FEM-SEM equivalence and additive Schwarz methods. The high-order operators are applied without forming the system matrix, making use of sum factorization for efficient evaluation. The system is preconditioned using a spectrally equivalent low-order ($p=1$) finite element operator discretization on a refined mesh. The low-order refined mesh is anisotropic and not shape regular in the polynomial degree of the high-order operator, ","authors_text":"Will Pazner","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-19T21:08:07Z","title":"Efficient low-order refined preconditioners for high-order matrix-free continuous and discontinuous Galerkin methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07071","kind":"arxiv","version":2},"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:aaec3cfbc336aeac01bfa07dc7608d2bc0020f6c8b7607cc7340175bebb5cc3d","target":"record","created_at":"2026-07-05T02:21:49Z","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":"8a843a11faf3ee563b460ed4ee7a46561e2943a6835169ddf6a061f28f66076f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-19T21:08:07Z","title_canon_sha256":"8966be0349fcef40c93857e1311cf3a4dc99ce04a63d0f89a92e1182546ce965"},"schema_version":"1.0","source":{"id":"1908.07071","kind":"arxiv","version":2}},"canonical_sha256":"ffc4136b991d15fc9f7d8261f96d7528cce31337a57511ad2d9b94c792d4196b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffc4136b991d15fc9f7d8261f96d7528cce31337a57511ad2d9b94c792d4196b","first_computed_at":"2026-07-05T02:21:49.782276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:21:49.782276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ixbD2zem8ZLUGSfByWqLZWHmpyKXR3WmS6jK4pHJ6Up5wV0iW4yUm2TtLv7bx6V2/7LfsxpyleiMiif/6JGsAg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:21:49.782755Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07071","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aaec3cfbc336aeac01bfa07dc7608d2bc0020f6c8b7607cc7340175bebb5cc3d","sha256:d45179c30df02e5a164c496e26b9a52836ddcf4f14a0a53dadd4e97a8263f56a"],"state_sha256":"5ab8d874eddce586c04ee61a5ba3a79f0a40eb7b8dd31e64d2f89f07753cb7a1"}