{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:C3WQWQP2OWXBT6AWJWOHXGIE5B","short_pith_number":"pith:C3WQWQP2","schema_version":"1.0","canonical_sha256":"16ed0b41fa75ae19f8164d9c7b9904e852e12334b5c8d2bfe81bf2d729e77bbe","source":{"kind":"arxiv","id":"2105.04080","version":4},"attestation_state":"computed","paper":{"title":"Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Thomas Y. Hou, Yifan Chen, Yixuan Wang","submitted_at":"2021-05-10T02:33:54Z","abstract_excerpt":"In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the wavenumber $k$ can be large. The main innovation is that our methods achieve a nearly exponential rate of convergence with respect to the computational degrees of freedom, using a coarse grid of mesh size $O(1/k)$ without suffering from the well-known pollution effect. The key idea is a non-overlapped domain decomposition and its associated coarse-fine scale decomposition of the solution space that adapts to the media pro"},"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":"2105.04080","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-05-10T02:33:54Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"f8cd8d9db5b154bf980084487467c4dc018e83204893e6272ec7f261fb1c1fef","abstract_canon_sha256":"39be5b7a8f2afb4691dd30bf1297ff18a66804471facb7f7f802a1e86d66c5d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:08:24.915807Z","signature_b64":"sPh+QUWVU2BXidNqOcVa54uKyx0lA0NVqbAbQvLT2On4fUbwG6S+bFE+Kxx2mpsGvpsnTo+Y3G2ReFVwnFm3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16ed0b41fa75ae19f8164d9c7b9904e852e12334b5c8d2bfe81bf2d729e77bbe","last_reissued_at":"2026-07-05T05:08:24.915392Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:08:24.915392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Thomas Y. Hou, Yifan Chen, Yixuan Wang","submitted_at":"2021-05-10T02:33:54Z","abstract_excerpt":"In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the wavenumber $k$ can be large. The main innovation is that our methods achieve a nearly exponential rate of convergence with respect to the computational degrees of freedom, using a coarse grid of mesh size $O(1/k)$ without suffering from the well-known pollution effect. The key idea is a non-overlapped domain decomposition and its associated coarse-fine scale decomposition of the solution space that adapts to the media pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.04080","kind":"arxiv","version":4},"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/2105.04080/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":"2105.04080","created_at":"2026-07-05T05:08:24.915446+00:00"},{"alias_kind":"arxiv_version","alias_value":"2105.04080v4","created_at":"2026-07-05T05:08:24.915446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.04080","created_at":"2026-07-05T05:08:24.915446+00:00"},{"alias_kind":"pith_short_12","alias_value":"C3WQWQP2OWXB","created_at":"2026-07-05T05:08:24.915446+00:00"},{"alias_kind":"pith_short_16","alias_value":"C3WQWQP2OWXBT6AW","created_at":"2026-07-05T05:08:24.915446+00:00"},{"alias_kind":"pith_short_8","alias_value":"C3WQWQP2","created_at":"2026-07-05T05:08:24.915446+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/C3WQWQP2OWXBT6AWJWOHXGIE5B","json":"https://pith.science/pith/C3WQWQP2OWXBT6AWJWOHXGIE5B.json","graph_json":"https://pith.science/api/pith-number/C3WQWQP2OWXBT6AWJWOHXGIE5B/graph.json","events_json":"https://pith.science/api/pith-number/C3WQWQP2OWXBT6AWJWOHXGIE5B/events.json","paper":"https://pith.science/paper/C3WQWQP2"},"agent_actions":{"view_html":"https://pith.science/pith/C3WQWQP2OWXBT6AWJWOHXGIE5B","download_json":"https://pith.science/pith/C3WQWQP2OWXBT6AWJWOHXGIE5B.json","view_paper":"https://pith.science/paper/C3WQWQP2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2105.04080&json=true","fetch_graph":"https://pith.science/api/pith-number/C3WQWQP2OWXBT6AWJWOHXGIE5B/graph.json","fetch_events":"https://pith.science/api/pith-number/C3WQWQP2OWXBT6AWJWOHXGIE5B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C3WQWQP2OWXBT6AWJWOHXGIE5B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C3WQWQP2OWXBT6AWJWOHXGIE5B/action/storage_attestation","attest_author":"https://pith.science/pith/C3WQWQP2OWXBT6AWJWOHXGIE5B/action/author_attestation","sign_citation":"https://pith.science/pith/C3WQWQP2OWXBT6AWJWOHXGIE5B/action/citation_signature","submit_replication":"https://pith.science/pith/C3WQWQP2OWXBT6AWJWOHXGIE5B/action/replication_record"}},"created_at":"2026-07-05T05:08:24.915446+00:00","updated_at":"2026-07-05T05:08:24.915446+00:00"}