{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:AFLPTYEK3E5IJGJW5G7KDJ4OYU","short_pith_number":"pith:AFLPTYEK","schema_version":"1.0","canonical_sha256":"0156f9e08ad93a849936e9bea1a78ec52cbca028137a40c1ec1aa3c7799fc3c1","source":{"kind":"arxiv","id":"1806.05848","version":1},"attestation_state":"computed","paper":{"title":"An efficient multigrid solver for isogeometric analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"\\'Alvaro P\\'e de la Riva, Carmen Rodrigo, Francisco J. Gaspar","submitted_at":"2018-06-15T08:14:49Z","abstract_excerpt":"The design of fast solvers for isogeometric analysis is receiving a lot of attention due to the challenge that offers to find an algorithm with a robust convergence with respect to the spline degree. Here, we analyze the application of geometric multigrid methods to this type of discretizations, and we propose a multigrid approach based on overlapping multiplicative Schwarz methods as smoothers. The size of the blocks considered within these relaxation procedures is adapted to the spline degree. A simple multigrid V-cycle with only one step of pre-smoothing results to be a very efficient algor"},"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":"1806.05848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-15T08:14:49Z","cross_cats_sorted":[],"title_canon_sha256":"2e5d9af13891c8e58c158115efc34cebbda4110a0b1912f54f78f0d0e0301884","abstract_canon_sha256":"274fbfc35909a1a9ea4a77366ba2a8a1d0f7caca1a1624891a1b141cf3b757e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:09.259048Z","signature_b64":"xW1sTHZcO9LHDPIQD/9zQClp8JPX6qK5xUtncMHKKYmZybX+VM0LhGkFpVLjDcwRGt1MljpS27bGbGTyHkjHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0156f9e08ad93a849936e9bea1a78ec52cbca028137a40c1ec1aa3c7799fc3c1","last_reissued_at":"2026-05-18T00:13:09.258380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:09.258380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An efficient multigrid solver for isogeometric analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"\\'Alvaro P\\'e de la Riva, Carmen Rodrigo, Francisco J. Gaspar","submitted_at":"2018-06-15T08:14:49Z","abstract_excerpt":"The design of fast solvers for isogeometric analysis is receiving a lot of attention due to the challenge that offers to find an algorithm with a robust convergence with respect to the spline degree. Here, we analyze the application of geometric multigrid methods to this type of discretizations, and we propose a multigrid approach based on overlapping multiplicative Schwarz methods as smoothers. The size of the blocks considered within these relaxation procedures is adapted to the spline degree. A simple multigrid V-cycle with only one step of pre-smoothing results to be a very efficient algor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05848","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":"1806.05848","created_at":"2026-05-18T00:13:09.258481+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.05848v1","created_at":"2026-05-18T00:13:09.258481+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05848","created_at":"2026-05-18T00:13:09.258481+00:00"},{"alias_kind":"pith_short_12","alias_value":"AFLPTYEK3E5I","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"AFLPTYEK3E5IJGJW","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"AFLPTYEK","created_at":"2026-05-18T12:32:13.499390+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/AFLPTYEK3E5IJGJW5G7KDJ4OYU","json":"https://pith.science/pith/AFLPTYEK3E5IJGJW5G7KDJ4OYU.json","graph_json":"https://pith.science/api/pith-number/AFLPTYEK3E5IJGJW5G7KDJ4OYU/graph.json","events_json":"https://pith.science/api/pith-number/AFLPTYEK3E5IJGJW5G7KDJ4OYU/events.json","paper":"https://pith.science/paper/AFLPTYEK"},"agent_actions":{"view_html":"https://pith.science/pith/AFLPTYEK3E5IJGJW5G7KDJ4OYU","download_json":"https://pith.science/pith/AFLPTYEK3E5IJGJW5G7KDJ4OYU.json","view_paper":"https://pith.science/paper/AFLPTYEK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.05848&json=true","fetch_graph":"https://pith.science/api/pith-number/AFLPTYEK3E5IJGJW5G7KDJ4OYU/graph.json","fetch_events":"https://pith.science/api/pith-number/AFLPTYEK3E5IJGJW5G7KDJ4OYU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AFLPTYEK3E5IJGJW5G7KDJ4OYU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AFLPTYEK3E5IJGJW5G7KDJ4OYU/action/storage_attestation","attest_author":"https://pith.science/pith/AFLPTYEK3E5IJGJW5G7KDJ4OYU/action/author_attestation","sign_citation":"https://pith.science/pith/AFLPTYEK3E5IJGJW5G7KDJ4OYU/action/citation_signature","submit_replication":"https://pith.science/pith/AFLPTYEK3E5IJGJW5G7KDJ4OYU/action/replication_record"}},"created_at":"2026-05-18T00:13:09.258481+00:00","updated_at":"2026-05-18T00:13:09.258481+00:00"}