{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:7SMV5O6MFYLQOC6R2T5XATVLJK","short_pith_number":"pith:7SMV5O6M","schema_version":"1.0","canonical_sha256":"fc995ebbcc2e17070bd1d4fb704eab4a8cb51a67e24bb5c4eed59b551ff8bb81","source":{"kind":"arxiv","id":"1708.06427","version":1},"attestation_state":"computed","paper":{"title":"A Bloch wave numerical scheme for scattering problems in periodic wave-guides","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ben Schweizer, Tom\\'a\\v{s} Dohnal","submitted_at":"2017-08-21T21:33:09Z","abstract_excerpt":"We present a new numerical scheme to solve the Helmholtz equation in a wave-guide. We consider a medium that is bounded in the $x_2$-direction, unbounded in the $x_1$-direction and $\\varepsilon$-periodic for large $|x_1|$, allowing different media on the left and on the right. We suggest a new numerical method that is based on a truncation of the domain and the use of Bloch wave ansatz functions in radiation boxes. We prove the existence and a stability estimate for the infinite dimensional version of the proposed problem. The scheme is tested on several interfaces of homogeneous and periodic "},"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":"1708.06427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-08-21T21:33:09Z","cross_cats_sorted":[],"title_canon_sha256":"d998bb06b495ebe013df6554ddb9e110c582746937b98e824a683098a162c790","abstract_canon_sha256":"e795f14569e34f46c6b36aea5971455775a7e122145d9f9549b872b900b70e5c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:41.557108Z","signature_b64":"XFUTRPuXL2/oCq5S9oPY/ICsv+tHIhnHdwULIdcporgTUEHgB+iQj7A+up+7Pn5QihzSng3wN4K0QNIWdTVGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc995ebbcc2e17070bd1d4fb704eab4a8cb51a67e24bb5c4eed59b551ff8bb81","last_reissued_at":"2026-05-18T00:37:41.556375Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:41.556375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Bloch wave numerical scheme for scattering problems in periodic wave-guides","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ben Schweizer, Tom\\'a\\v{s} Dohnal","submitted_at":"2017-08-21T21:33:09Z","abstract_excerpt":"We present a new numerical scheme to solve the Helmholtz equation in a wave-guide. We consider a medium that is bounded in the $x_2$-direction, unbounded in the $x_1$-direction and $\\varepsilon$-periodic for large $|x_1|$, allowing different media on the left and on the right. We suggest a new numerical method that is based on a truncation of the domain and the use of Bloch wave ansatz functions in radiation boxes. We prove the existence and a stability estimate for the infinite dimensional version of the proposed problem. The scheme is tested on several interfaces of homogeneous and periodic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06427","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":"1708.06427","created_at":"2026-05-18T00:37:41.556513+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.06427v1","created_at":"2026-05-18T00:37:41.556513+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06427","created_at":"2026-05-18T00:37:41.556513+00:00"},{"alias_kind":"pith_short_12","alias_value":"7SMV5O6MFYLQ","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"7SMV5O6MFYLQOC6R","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"7SMV5O6M","created_at":"2026-05-18T12:31:05.417338+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/7SMV5O6MFYLQOC6R2T5XATVLJK","json":"https://pith.science/pith/7SMV5O6MFYLQOC6R2T5XATVLJK.json","graph_json":"https://pith.science/api/pith-number/7SMV5O6MFYLQOC6R2T5XATVLJK/graph.json","events_json":"https://pith.science/api/pith-number/7SMV5O6MFYLQOC6R2T5XATVLJK/events.json","paper":"https://pith.science/paper/7SMV5O6M"},"agent_actions":{"view_html":"https://pith.science/pith/7SMV5O6MFYLQOC6R2T5XATVLJK","download_json":"https://pith.science/pith/7SMV5O6MFYLQOC6R2T5XATVLJK.json","view_paper":"https://pith.science/paper/7SMV5O6M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.06427&json=true","fetch_graph":"https://pith.science/api/pith-number/7SMV5O6MFYLQOC6R2T5XATVLJK/graph.json","fetch_events":"https://pith.science/api/pith-number/7SMV5O6MFYLQOC6R2T5XATVLJK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7SMV5O6MFYLQOC6R2T5XATVLJK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7SMV5O6MFYLQOC6R2T5XATVLJK/action/storage_attestation","attest_author":"https://pith.science/pith/7SMV5O6MFYLQOC6R2T5XATVLJK/action/author_attestation","sign_citation":"https://pith.science/pith/7SMV5O6MFYLQOC6R2T5XATVLJK/action/citation_signature","submit_replication":"https://pith.science/pith/7SMV5O6MFYLQOC6R2T5XATVLJK/action/replication_record"}},"created_at":"2026-05-18T00:37:41.556513+00:00","updated_at":"2026-05-18T00:37:41.556513+00:00"}