{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7IAIOP2ZGN6AOZA4HO2HI625A3","short_pith_number":"pith:7IAIOP2Z","schema_version":"1.0","canonical_sha256":"fa00873f59337c07641c3bb4747b5d06d9a05345eccae8f0f6358337bd64ae2a","source":{"kind":"arxiv","id":"1805.10058","version":1},"attestation_state":"computed","paper":{"title":"Isogeometric analysis for 2D and 3D curl-div problems: Spectral symbols and fast iterative solvers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ahmed Ratnani, Carla Manni, Hendrik Speleers, Mariarosa Mazza, Stefano Serra-Capizzano","submitted_at":"2018-05-25T09:39:43Z","abstract_excerpt":"Alfv\\'en-like operators are of interest in magnetohydrodynamics, which is used in plasma physics to study the macroscopic behavior of plasma. Motivated by this important and complex application, we focus on a parameter-dependent curl-div problem that can be seen as a prototype of an Alfv\\'en-like operator, and we discretize it using isogeometric analysis based on tensor-product B-splines. The involved coefficient matrices can be very ill-conditioned, so that standard numerical solution methods perform quite poorly here. In order to overcome the difficulties caused by such ill-conditioning, a t"},"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":"1805.10058","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-25T09:39:43Z","cross_cats_sorted":[],"title_canon_sha256":"eb139980c974f5d37d924b36082d0b62a328eaca0d9cdd9c74ed1500d26defb6","abstract_canon_sha256":"6527d5fb0257583095e2a1eb061834dec1666c4c3aa822bb335d502bbae99eb7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:41.302069Z","signature_b64":"uOYvlW6dF31Z21jx16rgbuXaW2De74Ir5LoM1+eNyl2xV3ariVEYRXkHajOVholBM8XC0xE/xZpPlLQC/ZvFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa00873f59337c07641c3bb4747b5d06d9a05345eccae8f0f6358337bd64ae2a","last_reissued_at":"2026-05-17T23:57:41.301629Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:41.301629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isogeometric analysis for 2D and 3D curl-div problems: Spectral symbols and fast iterative solvers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ahmed Ratnani, Carla Manni, Hendrik Speleers, Mariarosa Mazza, Stefano Serra-Capizzano","submitted_at":"2018-05-25T09:39:43Z","abstract_excerpt":"Alfv\\'en-like operators are of interest in magnetohydrodynamics, which is used in plasma physics to study the macroscopic behavior of plasma. Motivated by this important and complex application, we focus on a parameter-dependent curl-div problem that can be seen as a prototype of an Alfv\\'en-like operator, and we discretize it using isogeometric analysis based on tensor-product B-splines. The involved coefficient matrices can be very ill-conditioned, so that standard numerical solution methods perform quite poorly here. In order to overcome the difficulties caused by such ill-conditioning, a t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10058","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":""},"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":"1805.10058","created_at":"2026-05-17T23:57:41.301702+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.10058v1","created_at":"2026-05-17T23:57:41.301702+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10058","created_at":"2026-05-17T23:57:41.301702+00:00"},{"alias_kind":"pith_short_12","alias_value":"7IAIOP2ZGN6A","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"7IAIOP2ZGN6AOZA4","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"7IAIOP2Z","created_at":"2026-05-18T12:32:11.075285+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/7IAIOP2ZGN6AOZA4HO2HI625A3","json":"https://pith.science/pith/7IAIOP2ZGN6AOZA4HO2HI625A3.json","graph_json":"https://pith.science/api/pith-number/7IAIOP2ZGN6AOZA4HO2HI625A3/graph.json","events_json":"https://pith.science/api/pith-number/7IAIOP2ZGN6AOZA4HO2HI625A3/events.json","paper":"https://pith.science/paper/7IAIOP2Z"},"agent_actions":{"view_html":"https://pith.science/pith/7IAIOP2ZGN6AOZA4HO2HI625A3","download_json":"https://pith.science/pith/7IAIOP2ZGN6AOZA4HO2HI625A3.json","view_paper":"https://pith.science/paper/7IAIOP2Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.10058&json=true","fetch_graph":"https://pith.science/api/pith-number/7IAIOP2ZGN6AOZA4HO2HI625A3/graph.json","fetch_events":"https://pith.science/api/pith-number/7IAIOP2ZGN6AOZA4HO2HI625A3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7IAIOP2ZGN6AOZA4HO2HI625A3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7IAIOP2ZGN6AOZA4HO2HI625A3/action/storage_attestation","attest_author":"https://pith.science/pith/7IAIOP2ZGN6AOZA4HO2HI625A3/action/author_attestation","sign_citation":"https://pith.science/pith/7IAIOP2ZGN6AOZA4HO2HI625A3/action/citation_signature","submit_replication":"https://pith.science/pith/7IAIOP2ZGN6AOZA4HO2HI625A3/action/replication_record"}},"created_at":"2026-05-17T23:57:41.301702+00:00","updated_at":"2026-05-17T23:57:41.301702+00:00"}