{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:EPML4Z6WEQNOLVVRI7MVEZZEOB","short_pith_number":"pith:EPML4Z6W","schema_version":"1.0","canonical_sha256":"23d8be67d6241ae5d6b147d9526724704bb41fdf96208bc5b1dbc90d9e7603fb","source":{"kind":"arxiv","id":"1311.4257","version":1},"attestation_state":"computed","paper":{"title":"A parallel directional Fast Multipole Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Austin R. Benson, Bj\\\"orn Engquist, Jack Poulson, Kenneth Tran, Lexing Ying","submitted_at":"2013-11-18T03:47:36Z","abstract_excerpt":"This paper introduces a parallel directional fast multipole method (FMM) for solving N-body problems with highly oscillatory kernels, with a focus on the Helmholtz kernel in three dimensions. This class of oscillatory kernels requires a more restrictive low-rank criterion than that of the low-frequency regime, and thus effective parallelizations must adapt to the modified data dependencies. We propose a simple partition at a fixed level of the octree and show that, if the partitions are properly balanced between p processes, the overall runtime is essentially O(N log N/p+ p). By the structure "},"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":"1311.4257","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-18T03:47:36Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"112469212af4889dac30de847f9ce4d5c99d4a764fb9093f36805cd54af87c92","abstract_canon_sha256":"23081860f68188acb7487e9d2af4c4fe449e60d8f6f730b936117528a2fd72b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:47.530913Z","signature_b64":"OHOA6edTQ2hYd8KtGlQ8lgw0G9t1gV60JMP2tgEI23AUveXbrTPlqg+HwXDFZF5XDvRu9J9HsV3q2TQIHRvpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23d8be67d6241ae5d6b147d9526724704bb41fdf96208bc5b1dbc90d9e7603fb","last_reissued_at":"2026-05-18T00:26:47.530216Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:47.530216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A parallel directional Fast Multipole Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Austin R. Benson, Bj\\\"orn Engquist, Jack Poulson, Kenneth Tran, Lexing Ying","submitted_at":"2013-11-18T03:47:36Z","abstract_excerpt":"This paper introduces a parallel directional fast multipole method (FMM) for solving N-body problems with highly oscillatory kernels, with a focus on the Helmholtz kernel in three dimensions. This class of oscillatory kernels requires a more restrictive low-rank criterion than that of the low-frequency regime, and thus effective parallelizations must adapt to the modified data dependencies. We propose a simple partition at a fixed level of the octree and show that, if the partitions are properly balanced between p processes, the overall runtime is essentially O(N log N/p+ p). By the structure "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4257","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":"1311.4257","created_at":"2026-05-18T00:26:47.530337+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.4257v1","created_at":"2026-05-18T00:26:47.530337+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4257","created_at":"2026-05-18T00:26:47.530337+00:00"},{"alias_kind":"pith_short_12","alias_value":"EPML4Z6WEQNO","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EPML4Z6WEQNOLVVR","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EPML4Z6W","created_at":"2026-05-18T12:27:43.054852+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/EPML4Z6WEQNOLVVRI7MVEZZEOB","json":"https://pith.science/pith/EPML4Z6WEQNOLVVRI7MVEZZEOB.json","graph_json":"https://pith.science/api/pith-number/EPML4Z6WEQNOLVVRI7MVEZZEOB/graph.json","events_json":"https://pith.science/api/pith-number/EPML4Z6WEQNOLVVRI7MVEZZEOB/events.json","paper":"https://pith.science/paper/EPML4Z6W"},"agent_actions":{"view_html":"https://pith.science/pith/EPML4Z6WEQNOLVVRI7MVEZZEOB","download_json":"https://pith.science/pith/EPML4Z6WEQNOLVVRI7MVEZZEOB.json","view_paper":"https://pith.science/paper/EPML4Z6W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.4257&json=true","fetch_graph":"https://pith.science/api/pith-number/EPML4Z6WEQNOLVVRI7MVEZZEOB/graph.json","fetch_events":"https://pith.science/api/pith-number/EPML4Z6WEQNOLVVRI7MVEZZEOB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EPML4Z6WEQNOLVVRI7MVEZZEOB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EPML4Z6WEQNOLVVRI7MVEZZEOB/action/storage_attestation","attest_author":"https://pith.science/pith/EPML4Z6WEQNOLVVRI7MVEZZEOB/action/author_attestation","sign_citation":"https://pith.science/pith/EPML4Z6WEQNOLVVRI7MVEZZEOB/action/citation_signature","submit_replication":"https://pith.science/pith/EPML4Z6WEQNOLVVRI7MVEZZEOB/action/replication_record"}},"created_at":"2026-05-18T00:26:47.530337+00:00","updated_at":"2026-05-18T00:26:47.530337+00:00"}