{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:3ODXCW4BSVKMXMFPAI6BLTA3JH","short_pith_number":"pith:3ODXCW4B","schema_version":"1.0","canonical_sha256":"db87715b819554cbb0af023c15cc1b49d2372c7eaa13030ec3bd2d891b7636e8","source":{"kind":"arxiv","id":"1811.01264","version":1},"attestation_state":"computed","paper":{"title":"Monolithic mixed-dimensional multigrid methods for single-phase flow in fractured porous media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andr\\'es Arrar\\'as, Carmen Rodrigo, Francisco J. Gaspar, Laura Portero","submitted_at":"2018-11-03T18:37:52Z","abstract_excerpt":"This paper deals with the efficient numerical solution of single-phase flow problems in fractured porous media. A monolithic multigrid method is proposed for solving two-dimensional arbitrary fracture networks with vertical and/or horizontal possibly intersecting fractures. The key point is to combine two-dimensional multigrid components (smoother and inter-grid transfer operators) in the porous matrix with their one-dimensional counterparts within the fractures, giving rise to a mixed-dimensional multigrid method. This combination seems to be optimal since it provides an algorithm whose conve"},"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":"1811.01264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-03T18:37:52Z","cross_cats_sorted":[],"title_canon_sha256":"22899fcd1ae512ab345f14e5ce6d73a6b719c4271933751c8ded66e242b3d022","abstract_canon_sha256":"046453a469506fc89efee687182c3b061a702564a578f7873f9d4339190f9b08"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:34.804120Z","signature_b64":"O6XZONWvxsy3/EPWymC0wY1VDvcGZEoGeMAhGZ50vfNiAbbvOi6xoevcFxxeycI+Xi2Yr1LF6bYALcvf3fJ8BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db87715b819554cbb0af023c15cc1b49d2372c7eaa13030ec3bd2d891b7636e8","last_reissued_at":"2026-05-18T00:01:34.803607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:34.803607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monolithic mixed-dimensional multigrid methods for single-phase flow in fractured porous media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andr\\'es Arrar\\'as, Carmen Rodrigo, Francisco J. Gaspar, Laura Portero","submitted_at":"2018-11-03T18:37:52Z","abstract_excerpt":"This paper deals with the efficient numerical solution of single-phase flow problems in fractured porous media. A monolithic multigrid method is proposed for solving two-dimensional arbitrary fracture networks with vertical and/or horizontal possibly intersecting fractures. The key point is to combine two-dimensional multigrid components (smoother and inter-grid transfer operators) in the porous matrix with their one-dimensional counterparts within the fractures, giving rise to a mixed-dimensional multigrid method. This combination seems to be optimal since it provides an algorithm whose conve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01264","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":"1811.01264","created_at":"2026-05-18T00:01:34.803685+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.01264v1","created_at":"2026-05-18T00:01:34.803685+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01264","created_at":"2026-05-18T00:01:34.803685+00:00"},{"alias_kind":"pith_short_12","alias_value":"3ODXCW4BSVKM","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"3ODXCW4BSVKMXMFP","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"3ODXCW4B","created_at":"2026-05-18T12:32:02.567920+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/3ODXCW4BSVKMXMFPAI6BLTA3JH","json":"https://pith.science/pith/3ODXCW4BSVKMXMFPAI6BLTA3JH.json","graph_json":"https://pith.science/api/pith-number/3ODXCW4BSVKMXMFPAI6BLTA3JH/graph.json","events_json":"https://pith.science/api/pith-number/3ODXCW4BSVKMXMFPAI6BLTA3JH/events.json","paper":"https://pith.science/paper/3ODXCW4B"},"agent_actions":{"view_html":"https://pith.science/pith/3ODXCW4BSVKMXMFPAI6BLTA3JH","download_json":"https://pith.science/pith/3ODXCW4BSVKMXMFPAI6BLTA3JH.json","view_paper":"https://pith.science/paper/3ODXCW4B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.01264&json=true","fetch_graph":"https://pith.science/api/pith-number/3ODXCW4BSVKMXMFPAI6BLTA3JH/graph.json","fetch_events":"https://pith.science/api/pith-number/3ODXCW4BSVKMXMFPAI6BLTA3JH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3ODXCW4BSVKMXMFPAI6BLTA3JH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3ODXCW4BSVKMXMFPAI6BLTA3JH/action/storage_attestation","attest_author":"https://pith.science/pith/3ODXCW4BSVKMXMFPAI6BLTA3JH/action/author_attestation","sign_citation":"https://pith.science/pith/3ODXCW4BSVKMXMFPAI6BLTA3JH/action/citation_signature","submit_replication":"https://pith.science/pith/3ODXCW4BSVKMXMFPAI6BLTA3JH/action/replication_record"}},"created_at":"2026-05-18T00:01:34.803685+00:00","updated_at":"2026-05-18T00:01:34.803685+00:00"}