{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LAZIID4N3P3WJON7ZOL2Y2ZTPL","short_pith_number":"pith:LAZIID4N","schema_version":"1.0","canonical_sha256":"5832840f8ddbf764b9bfcb97ac6b337ad483bc8ddba76cc01b07b6cf0c5c765a","source":{"kind":"arxiv","id":"1803.02075","version":2},"attestation_state":"computed","paper":{"title":"Development of a New Spectral Collocation Method Using Laplacian Eigenbasis for Elliptic Partial Differential Equations in an Extended Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Cheng-Hong Robert Kao, Po-Yi Wu, Tony Wen-Hann Sheu","submitted_at":"2018-03-06T09:42:14Z","abstract_excerpt":"The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle geometrically complicated problems. However, the convergence is deteriorated when embedded boundary strategies are employed. Owing to the loss of regularity, in this paper we propose a new spectral collocation method which retains the regularity of solutions to solve differential equations in the case of complex geometries. The idea is rooted in the basis functions de"},"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":"1803.02075","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-06T09:42:14Z","cross_cats_sorted":[],"title_canon_sha256":"23046061b847dd4761915252537e93af2d72938aadc72c773d78abfbc5a50dbd","abstract_canon_sha256":"1be71290f26b63d1ffa012818a8294eb5f778f2513b7deccf83b63e0a1a31cd2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:50.505477Z","signature_b64":"4XeywLSpmQ3KmuxPebEphBslJNXBKu2bFMgqyg/9AoUrDrG8pYvFo/abesxW8vghUR6CP1QHYaB/y4qd836UCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5832840f8ddbf764b9bfcb97ac6b337ad483bc8ddba76cc01b07b6cf0c5c765a","last_reissued_at":"2026-05-18T00:21:50.504893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:50.504893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Development of a New Spectral Collocation Method Using Laplacian Eigenbasis for Elliptic Partial Differential Equations in an Extended Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Cheng-Hong Robert Kao, Po-Yi Wu, Tony Wen-Hann Sheu","submitted_at":"2018-03-06T09:42:14Z","abstract_excerpt":"The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle geometrically complicated problems. However, the convergence is deteriorated when embedded boundary strategies are employed. Owing to the loss of regularity, in this paper we propose a new spectral collocation method which retains the regularity of solutions to solve differential equations in the case of complex geometries. The idea is rooted in the basis functions de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02075","kind":"arxiv","version":2},"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":"1803.02075","created_at":"2026-05-18T00:21:50.504981+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.02075v2","created_at":"2026-05-18T00:21:50.504981+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02075","created_at":"2026-05-18T00:21:50.504981+00:00"},{"alias_kind":"pith_short_12","alias_value":"LAZIID4N3P3W","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"LAZIID4N3P3WJON7","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"LAZIID4N","created_at":"2026-05-18T12:32:33.847187+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/LAZIID4N3P3WJON7ZOL2Y2ZTPL","json":"https://pith.science/pith/LAZIID4N3P3WJON7ZOL2Y2ZTPL.json","graph_json":"https://pith.science/api/pith-number/LAZIID4N3P3WJON7ZOL2Y2ZTPL/graph.json","events_json":"https://pith.science/api/pith-number/LAZIID4N3P3WJON7ZOL2Y2ZTPL/events.json","paper":"https://pith.science/paper/LAZIID4N"},"agent_actions":{"view_html":"https://pith.science/pith/LAZIID4N3P3WJON7ZOL2Y2ZTPL","download_json":"https://pith.science/pith/LAZIID4N3P3WJON7ZOL2Y2ZTPL.json","view_paper":"https://pith.science/paper/LAZIID4N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.02075&json=true","fetch_graph":"https://pith.science/api/pith-number/LAZIID4N3P3WJON7ZOL2Y2ZTPL/graph.json","fetch_events":"https://pith.science/api/pith-number/LAZIID4N3P3WJON7ZOL2Y2ZTPL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LAZIID4N3P3WJON7ZOL2Y2ZTPL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LAZIID4N3P3WJON7ZOL2Y2ZTPL/action/storage_attestation","attest_author":"https://pith.science/pith/LAZIID4N3P3WJON7ZOL2Y2ZTPL/action/author_attestation","sign_citation":"https://pith.science/pith/LAZIID4N3P3WJON7ZOL2Y2ZTPL/action/citation_signature","submit_replication":"https://pith.science/pith/LAZIID4N3P3WJON7ZOL2Y2ZTPL/action/replication_record"}},"created_at":"2026-05-18T00:21:50.504981+00:00","updated_at":"2026-05-18T00:21:50.504981+00:00"}