{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:DC7YXCV7JJWWHM7VGHJJVCLABJ","short_pith_number":"pith:DC7YXCV7","schema_version":"1.0","canonical_sha256":"18bf8b8abf4a6d63b3f531d29a89600a5217fcff6382a1e3d3484ccb33126258","source":{"kind":"arxiv","id":"1607.01822","version":1},"attestation_state":"computed","paper":{"title":"An Adaptive Multiresoluton Discontinuous Galerkin Method for Time-Dependent Transport Equations in Multi-dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Wei Guo, Yingda Cheng","submitted_at":"2016-07-06T21:53:52Z","abstract_excerpt":"In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for time-dependent transport equations in multi-dimensions. The method is constructed using multiwavlelets on tensorized nested grids. Adaptivity is realized by error thresholding based on the hierarchical surplus, and the Runge-Kutta DG (RKDG) scheme is employed as the reference time evolution algorithm. We show that the scheme performs similarly to a sparse grid DG method when the solution is smooth, reducing computational cost in multi-dimensions. When the solution is no longer smooth, the adaptive algo"},"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":"1607.01822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-06T21:53:52Z","cross_cats_sorted":[],"title_canon_sha256":"8399f598c588c81056f4888b1339c1e442f72028161a7a3bc70753394289371b","abstract_canon_sha256":"0bc1c84eeb3cff64ea323062c0c56b4bc1d2ec0e7838b14cf0e595f81f8f34bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:23.200483Z","signature_b64":"tEHJV/CjVodKkI/mAzEfEY6kxmkjvwgGPW28EHtMD07M4GUy7IenHWQaaRgbU3XX8qAJfvxZdgd00DEnJ8BRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18bf8b8abf4a6d63b3f531d29a89600a5217fcff6382a1e3d3484ccb33126258","last_reissued_at":"2026-05-18T01:11:23.200042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:23.200042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Adaptive Multiresoluton Discontinuous Galerkin Method for Time-Dependent Transport Equations in Multi-dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Wei Guo, Yingda Cheng","submitted_at":"2016-07-06T21:53:52Z","abstract_excerpt":"In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for time-dependent transport equations in multi-dimensions. The method is constructed using multiwavlelets on tensorized nested grids. Adaptivity is realized by error thresholding based on the hierarchical surplus, and the Runge-Kutta DG (RKDG) scheme is employed as the reference time evolution algorithm. We show that the scheme performs similarly to a sparse grid DG method when the solution is smooth, reducing computational cost in multi-dimensions. When the solution is no longer smooth, the adaptive algo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01822","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":"1607.01822","created_at":"2026-05-18T01:11:23.200118+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.01822v1","created_at":"2026-05-18T01:11:23.200118+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01822","created_at":"2026-05-18T01:11:23.200118+00:00"},{"alias_kind":"pith_short_12","alias_value":"DC7YXCV7JJWW","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"DC7YXCV7JJWWHM7V","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"DC7YXCV7","created_at":"2026-05-18T12:30:12.583610+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/DC7YXCV7JJWWHM7VGHJJVCLABJ","json":"https://pith.science/pith/DC7YXCV7JJWWHM7VGHJJVCLABJ.json","graph_json":"https://pith.science/api/pith-number/DC7YXCV7JJWWHM7VGHJJVCLABJ/graph.json","events_json":"https://pith.science/api/pith-number/DC7YXCV7JJWWHM7VGHJJVCLABJ/events.json","paper":"https://pith.science/paper/DC7YXCV7"},"agent_actions":{"view_html":"https://pith.science/pith/DC7YXCV7JJWWHM7VGHJJVCLABJ","download_json":"https://pith.science/pith/DC7YXCV7JJWWHM7VGHJJVCLABJ.json","view_paper":"https://pith.science/paper/DC7YXCV7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.01822&json=true","fetch_graph":"https://pith.science/api/pith-number/DC7YXCV7JJWWHM7VGHJJVCLABJ/graph.json","fetch_events":"https://pith.science/api/pith-number/DC7YXCV7JJWWHM7VGHJJVCLABJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DC7YXCV7JJWWHM7VGHJJVCLABJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DC7YXCV7JJWWHM7VGHJJVCLABJ/action/storage_attestation","attest_author":"https://pith.science/pith/DC7YXCV7JJWWHM7VGHJJVCLABJ/action/author_attestation","sign_citation":"https://pith.science/pith/DC7YXCV7JJWWHM7VGHJJVCLABJ/action/citation_signature","submit_replication":"https://pith.science/pith/DC7YXCV7JJWWHM7VGHJJVCLABJ/action/replication_record"}},"created_at":"2026-05-18T01:11:23.200118+00:00","updated_at":"2026-05-18T01:11:23.200118+00:00"}