{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LMJIKEUIV4OMH5I2YHZKDMUQTW","short_pith_number":"pith:LMJIKEUI","schema_version":"1.0","canonical_sha256":"5b12851288af1cc3f51ac1f2a1b2909dac2d5a54ef775a101e8abe9245511401","source":{"kind":"arxiv","id":"1607.05035","version":1},"attestation_state":"computed","paper":{"title":"Robust Multigrid for Isogeometric Analysis Based on Stable Splittings of Spline Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Clemens Hofreither, Stefan Takacs","submitted_at":"2016-07-18T12:07:22Z","abstract_excerpt":"We present a robust and efficient multigrid method for single-patch isogeometric discretizations using tensor product B-splines of maximum smoothness. Our method is based on a stable splitting of the spline space into a large subspace of interior splines which satisfy a robust inverse inequality, as well as one or several smaller subspaces which capture the boundary effects responsible for the spectral outliers which occur in Isogeometric Analysis. We then construct a multigrid smoother based on an additive subspace correction approach, applying a different smoother to each of the subspaces. F"},"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":"1607.05035","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-18T12:07:22Z","cross_cats_sorted":[],"title_canon_sha256":"31d9bb54b490c7bba6def422b91d365e47cef42ba2baae757576dfb95051ed94","abstract_canon_sha256":"9772d60d1ffffc17f1ddb7df678a8390757225dd001e4f63acfb12113b117af8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:48.373173Z","signature_b64":"jm8RMU2Zia+ZRBdbku/T2f+XYxIOpKF7fJ7m2Z25uDe821QelRXjRVNHkJMSn9sNfotMT9Cb1a6a3yC4w2qFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b12851288af1cc3f51ac1f2a1b2909dac2d5a54ef775a101e8abe9245511401","last_reissued_at":"2026-05-18T00:37:48.372435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:48.372435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Robust Multigrid for Isogeometric Analysis Based on Stable Splittings of Spline Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Clemens Hofreither, Stefan Takacs","submitted_at":"2016-07-18T12:07:22Z","abstract_excerpt":"We present a robust and efficient multigrid method for single-patch isogeometric discretizations using tensor product B-splines of maximum smoothness. Our method is based on a stable splitting of the spline space into a large subspace of interior splines which satisfy a robust inverse inequality, as well as one or several smaller subspaces which capture the boundary effects responsible for the spectral outliers which occur in Isogeometric Analysis. We then construct a multigrid smoother based on an additive subspace correction approach, applying a different smoother to each of the subspaces. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05035","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":"1607.05035","created_at":"2026-05-18T00:37:48.372542+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.05035v1","created_at":"2026-05-18T00:37:48.372542+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05035","created_at":"2026-05-18T00:37:48.372542+00:00"},{"alias_kind":"pith_short_12","alias_value":"LMJIKEUIV4OM","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LMJIKEUIV4OMH5I2","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LMJIKEUI","created_at":"2026-05-18T12:30:29.479603+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/LMJIKEUIV4OMH5I2YHZKDMUQTW","json":"https://pith.science/pith/LMJIKEUIV4OMH5I2YHZKDMUQTW.json","graph_json":"https://pith.science/api/pith-number/LMJIKEUIV4OMH5I2YHZKDMUQTW/graph.json","events_json":"https://pith.science/api/pith-number/LMJIKEUIV4OMH5I2YHZKDMUQTW/events.json","paper":"https://pith.science/paper/LMJIKEUI"},"agent_actions":{"view_html":"https://pith.science/pith/LMJIKEUIV4OMH5I2YHZKDMUQTW","download_json":"https://pith.science/pith/LMJIKEUIV4OMH5I2YHZKDMUQTW.json","view_paper":"https://pith.science/paper/LMJIKEUI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.05035&json=true","fetch_graph":"https://pith.science/api/pith-number/LMJIKEUIV4OMH5I2YHZKDMUQTW/graph.json","fetch_events":"https://pith.science/api/pith-number/LMJIKEUIV4OMH5I2YHZKDMUQTW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LMJIKEUIV4OMH5I2YHZKDMUQTW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LMJIKEUIV4OMH5I2YHZKDMUQTW/action/storage_attestation","attest_author":"https://pith.science/pith/LMJIKEUIV4OMH5I2YHZKDMUQTW/action/author_attestation","sign_citation":"https://pith.science/pith/LMJIKEUIV4OMH5I2YHZKDMUQTW/action/citation_signature","submit_replication":"https://pith.science/pith/LMJIKEUIV4OMH5I2YHZKDMUQTW/action/replication_record"}},"created_at":"2026-05-18T00:37:48.372542+00:00","updated_at":"2026-05-18T00:37:48.372542+00:00"}