{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:66PJX4HWHOUTPOX4MUM3263ANT","short_pith_number":"pith:66PJX4HW","schema_version":"1.0","canonical_sha256":"f79e9bf0f63ba937bafc6519bd7b606cd04bffe6e274c370e134352b3c285d1f","source":{"kind":"arxiv","id":"2502.07569","version":1},"attestation_state":"computed","paper":{"title":"Efficient finite element methods for semiclassical nonlinear Schr\\\"odinger equations with random potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Panchi Li, Zhiwen Zhang","submitted_at":"2025-02-11T14:08:35Z","abstract_excerpt":"In this paper, we propose two time-splitting finite element methods to solve the semiclassical nonlinear Schr\\\"odinger equation (NLSE) with random potentials. We then introduce the multiscale finite element method (MsFEM) to reduce the degrees of freedom in the physical space. We construct multiscale basis functions by solving optimization problems and rigorously analyze two time-splitting MsFEMs for the semiclassical NLSE with random potentials. We provide the $L^2$ error estimate of the proposed methods and show that they achieve second-order accuracy in both spatial and temporal spaces and "},"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":"2502.07569","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-02-11T14:08:35Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6c9e75525c07d511231c8806c876181723a2b7018b525a6355f2fe39a0e7129f","abstract_canon_sha256":"7ce7e3761844495d8edd3bf068f164ed0e71281aa93bcc2d7a754a562a8afea1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:12:39.470073Z","signature_b64":"nSeO4zxVs/Xs4h0WNVY2KJ6a8vaaQH80oRdgjBEM16UOakFNHR2/wtuusJ0MoCmj0lp8OUoQiMhl/1ws+wVLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f79e9bf0f63ba937bafc6519bd7b606cd04bffe6e274c370e134352b3c285d1f","last_reissued_at":"2026-07-05T10:12:39.469584Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:12:39.469584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient finite element methods for semiclassical nonlinear Schr\\\"odinger equations with random potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Panchi Li, Zhiwen Zhang","submitted_at":"2025-02-11T14:08:35Z","abstract_excerpt":"In this paper, we propose two time-splitting finite element methods to solve the semiclassical nonlinear Schr\\\"odinger equation (NLSE) with random potentials. We then introduce the multiscale finite element method (MsFEM) to reduce the degrees of freedom in the physical space. We construct multiscale basis functions by solving optimization problems and rigorously analyze two time-splitting MsFEMs for the semiclassical NLSE with random potentials. We provide the $L^2$ error estimate of the proposed methods and show that they achieve second-order accuracy in both spatial and temporal spaces and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07569","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/2502.07569/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":"2502.07569","created_at":"2026-07-05T10:12:39.469641+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.07569v1","created_at":"2026-07-05T10:12:39.469641+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07569","created_at":"2026-07-05T10:12:39.469641+00:00"},{"alias_kind":"pith_short_12","alias_value":"66PJX4HWHOUT","created_at":"2026-07-05T10:12:39.469641+00:00"},{"alias_kind":"pith_short_16","alias_value":"66PJX4HWHOUTPOX4","created_at":"2026-07-05T10:12:39.469641+00:00"},{"alias_kind":"pith_short_8","alias_value":"66PJX4HW","created_at":"2026-07-05T10:12:39.469641+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.16647","citing_title":"A quasi-Monte Carlo multiscale method for the wave propagation in random media","ref_index":33,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/66PJX4HWHOUTPOX4MUM3263ANT","json":"https://pith.science/pith/66PJX4HWHOUTPOX4MUM3263ANT.json","graph_json":"https://pith.science/api/pith-number/66PJX4HWHOUTPOX4MUM3263ANT/graph.json","events_json":"https://pith.science/api/pith-number/66PJX4HWHOUTPOX4MUM3263ANT/events.json","paper":"https://pith.science/paper/66PJX4HW"},"agent_actions":{"view_html":"https://pith.science/pith/66PJX4HWHOUTPOX4MUM3263ANT","download_json":"https://pith.science/pith/66PJX4HWHOUTPOX4MUM3263ANT.json","view_paper":"https://pith.science/paper/66PJX4HW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.07569&json=true","fetch_graph":"https://pith.science/api/pith-number/66PJX4HWHOUTPOX4MUM3263ANT/graph.json","fetch_events":"https://pith.science/api/pith-number/66PJX4HWHOUTPOX4MUM3263ANT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/66PJX4HWHOUTPOX4MUM3263ANT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/66PJX4HWHOUTPOX4MUM3263ANT/action/storage_attestation","attest_author":"https://pith.science/pith/66PJX4HWHOUTPOX4MUM3263ANT/action/author_attestation","sign_citation":"https://pith.science/pith/66PJX4HWHOUTPOX4MUM3263ANT/action/citation_signature","submit_replication":"https://pith.science/pith/66PJX4HWHOUTPOX4MUM3263ANT/action/replication_record"}},"created_at":"2026-07-05T10:12:39.469641+00:00","updated_at":"2026-07-05T10:12:39.469641+00:00"}