{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:QKOYPZ3TFMVDFYYZ7P2RFSDZU3","short_pith_number":"pith:QKOYPZ3T","schema_version":"1.0","canonical_sha256":"829d87e7732b2a32e319fbf512c879a6caef7c181e1a138021415114b1c165f6","source":{"kind":"arxiv","id":"2202.13552","version":1},"attestation_state":"computed","paper":{"title":"Effect of Choices of Boundary Conditions on the Numerical Efficiency of Direct Solutions of Finite Difference frequency Domain Systems with Perfectly Matched Layers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Nathan Zhao, Shanhui Fan","submitted_at":"2022-02-28T05:39:20Z","abstract_excerpt":"Direct solvers are a common method for solving finite difference frequency domain (FDFD) systems that arise in numerical solutions of Maxwell's equations. In a direct solver, one factorizes the system matrix. Since the system matrix is typically very sparse, the fill-in of these factors is the single most important computational consideration in terms of time complexity and memory requirements. As a result, it is of great interest to determine ways in which this fill-in can be systematically reduced. In this paper, we show that in the context of commonly used perfectly matched boundary layer m"},"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":"2202.13552","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-02-28T05:39:20Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"84cce017802ee5eb2ea5674759d25979303a0c885b68dacfb4ed5d8bf9d9a786","abstract_canon_sha256":"ee2d0742609b04bcbcbf50d5f8a0a63b35a89a1029a5b90388df396b3ee5fa57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:43:40.238446Z","signature_b64":"mlVM2zs0txXCb9X3L8WYZYKYnHrT9Rz4P8W+8f/QFgeJRU/5PcQqYwQOZRh8gDmZI3YRvgZqxaLOdDCtXjjBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"829d87e7732b2a32e319fbf512c879a6caef7c181e1a138021415114b1c165f6","last_reissued_at":"2026-07-05T04:43:40.238032Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:43:40.238032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Effect of Choices of Boundary Conditions on the Numerical Efficiency of Direct Solutions of Finite Difference frequency Domain Systems with Perfectly Matched Layers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Nathan Zhao, Shanhui Fan","submitted_at":"2022-02-28T05:39:20Z","abstract_excerpt":"Direct solvers are a common method for solving finite difference frequency domain (FDFD) systems that arise in numerical solutions of Maxwell's equations. In a direct solver, one factorizes the system matrix. Since the system matrix is typically very sparse, the fill-in of these factors is the single most important computational consideration in terms of time complexity and memory requirements. As a result, it is of great interest to determine ways in which this fill-in can be systematically reduced. In this paper, we show that in the context of commonly used perfectly matched boundary layer m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.13552","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.13552/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2202.13552","created_at":"2026-07-05T04:43:40.238086+00:00"},{"alias_kind":"arxiv_version","alias_value":"2202.13552v1","created_at":"2026-07-05T04:43:40.238086+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.13552","created_at":"2026-07-05T04:43:40.238086+00:00"},{"alias_kind":"pith_short_12","alias_value":"QKOYPZ3TFMVD","created_at":"2026-07-05T04:43:40.238086+00:00"},{"alias_kind":"pith_short_16","alias_value":"QKOYPZ3TFMVDFYYZ","created_at":"2026-07-05T04:43:40.238086+00:00"},{"alias_kind":"pith_short_8","alias_value":"QKOYPZ3T","created_at":"2026-07-05T04:43:40.238086+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/QKOYPZ3TFMVDFYYZ7P2RFSDZU3","json":"https://pith.science/pith/QKOYPZ3TFMVDFYYZ7P2RFSDZU3.json","graph_json":"https://pith.science/api/pith-number/QKOYPZ3TFMVDFYYZ7P2RFSDZU3/graph.json","events_json":"https://pith.science/api/pith-number/QKOYPZ3TFMVDFYYZ7P2RFSDZU3/events.json","paper":"https://pith.science/paper/QKOYPZ3T"},"agent_actions":{"view_html":"https://pith.science/pith/QKOYPZ3TFMVDFYYZ7P2RFSDZU3","download_json":"https://pith.science/pith/QKOYPZ3TFMVDFYYZ7P2RFSDZU3.json","view_paper":"https://pith.science/paper/QKOYPZ3T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2202.13552&json=true","fetch_graph":"https://pith.science/api/pith-number/QKOYPZ3TFMVDFYYZ7P2RFSDZU3/graph.json","fetch_events":"https://pith.science/api/pith-number/QKOYPZ3TFMVDFYYZ7P2RFSDZU3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QKOYPZ3TFMVDFYYZ7P2RFSDZU3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QKOYPZ3TFMVDFYYZ7P2RFSDZU3/action/storage_attestation","attest_author":"https://pith.science/pith/QKOYPZ3TFMVDFYYZ7P2RFSDZU3/action/author_attestation","sign_citation":"https://pith.science/pith/QKOYPZ3TFMVDFYYZ7P2RFSDZU3/action/citation_signature","submit_replication":"https://pith.science/pith/QKOYPZ3TFMVDFYYZ7P2RFSDZU3/action/replication_record"}},"created_at":"2026-07-05T04:43:40.238086+00:00","updated_at":"2026-07-05T04:43:40.238086+00:00"}