{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:7VIMVUUIQVAAYMLCA2IVU6E3WF","short_pith_number":"pith:7VIMVUUI","schema_version":"1.0","canonical_sha256":"fd50cad28885400c316206915a789bb1640bb8ff758ffe1c49cd5d95d375a810","source":{"kind":"arxiv","id":"1907.01790","version":1},"attestation_state":"computed","paper":{"title":"BPX preconditioners for isogeometric analysis using analysis-suitable T-splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Durkbin Cho, Rafael V\\'azquez","submitted_at":"2019-07-03T08:38:53Z","abstract_excerpt":"We propose and analyze optimal additive multilevel solvers for isogeometric discretizations of scalar elliptic problems for locally refined T-meshes. Applying the refinement strategy in Morgenstern and Peterseim (2015, Comput. Aided Geom. Design, 34, 50-66) we can guarantee that the obtained T-meshes have a multilevel structure, and that the associated T-splines are analysis-suitable, for which we can define a dual basis and a stable projector. Taking advantage of the multilevel structure, we develop two BPX preconditioners: the first on the basis of local smoothing only for the functions affe"},"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":"1907.01790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-07-03T08:38:53Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"04647701d345a06ede9fb44447e4425df5380f5b3845b404d2e40aca829c3d11","abstract_canon_sha256":"4ec9e4edef5ab1fc9dfb6f6d5cf58525491d4429bd5ecbec66a98fcc8f24b46c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:35.073213Z","signature_b64":"Jsy0lEGLESYzxgWjW3JiHnx0lLjGoCmeGk5hburifeeS2CsNfnrPbuOuJGAP+wylQmqvt5dSIfZu11pS79R+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd50cad28885400c316206915a789bb1640bb8ff758ffe1c49cd5d95d375a810","last_reissued_at":"2026-05-17T23:41:35.072549Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:35.072549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"BPX preconditioners for isogeometric analysis using analysis-suitable T-splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Durkbin Cho, Rafael V\\'azquez","submitted_at":"2019-07-03T08:38:53Z","abstract_excerpt":"We propose and analyze optimal additive multilevel solvers for isogeometric discretizations of scalar elliptic problems for locally refined T-meshes. Applying the refinement strategy in Morgenstern and Peterseim (2015, Comput. Aided Geom. Design, 34, 50-66) we can guarantee that the obtained T-meshes have a multilevel structure, and that the associated T-splines are analysis-suitable, for which we can define a dual basis and a stable projector. Taking advantage of the multilevel structure, we develop two BPX preconditioners: the first on the basis of local smoothing only for the functions affe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01790","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":"1907.01790","created_at":"2026-05-17T23:41:35.072640+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.01790v1","created_at":"2026-05-17T23:41:35.072640+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01790","created_at":"2026-05-17T23:41:35.072640+00:00"},{"alias_kind":"pith_short_12","alias_value":"7VIMVUUIQVAA","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"7VIMVUUIQVAAYMLC","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"7VIMVUUI","created_at":"2026-05-18T12:33:12.712433+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/7VIMVUUIQVAAYMLCA2IVU6E3WF","json":"https://pith.science/pith/7VIMVUUIQVAAYMLCA2IVU6E3WF.json","graph_json":"https://pith.science/api/pith-number/7VIMVUUIQVAAYMLCA2IVU6E3WF/graph.json","events_json":"https://pith.science/api/pith-number/7VIMVUUIQVAAYMLCA2IVU6E3WF/events.json","paper":"https://pith.science/paper/7VIMVUUI"},"agent_actions":{"view_html":"https://pith.science/pith/7VIMVUUIQVAAYMLCA2IVU6E3WF","download_json":"https://pith.science/pith/7VIMVUUIQVAAYMLCA2IVU6E3WF.json","view_paper":"https://pith.science/paper/7VIMVUUI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.01790&json=true","fetch_graph":"https://pith.science/api/pith-number/7VIMVUUIQVAAYMLCA2IVU6E3WF/graph.json","fetch_events":"https://pith.science/api/pith-number/7VIMVUUIQVAAYMLCA2IVU6E3WF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7VIMVUUIQVAAYMLCA2IVU6E3WF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7VIMVUUIQVAAYMLCA2IVU6E3WF/action/storage_attestation","attest_author":"https://pith.science/pith/7VIMVUUIQVAAYMLCA2IVU6E3WF/action/author_attestation","sign_citation":"https://pith.science/pith/7VIMVUUIQVAAYMLCA2IVU6E3WF/action/citation_signature","submit_replication":"https://pith.science/pith/7VIMVUUIQVAAYMLCA2IVU6E3WF/action/replication_record"}},"created_at":"2026-05-17T23:41:35.072640+00:00","updated_at":"2026-05-17T23:41:35.072640+00:00"}