{"created":"2025-01-19T01:19:17.256710+00:00","updated":"2025-01-19T14:58:48.625508+00:00","metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00218945","sets":["1164:2240:10902:10971"]},"path":["10971"],"owner":"44499","recid":"218945","title":["MGRITの粗格子演算子に対するRunge-Kutta法の係数最適化とその高速化"],"pubdate":{"attribute_name":"公開日","attribute_value":"2022-07-20"},"_buckets":{"deposit":"ba8b5915-0667-415f-abd0-aec6a231d8ef"},"_deposit":{"id":"218945","pid":{"type":"depid","value":"218945","revision_id":0},"owners":[44499],"status":"published","created_by":44499},"item_title":"MGRITの粗格子演算子に対するRunge-Kutta法の係数最適化とその高速化","author_link":["570428","570427","570429","570430"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"MGRITの粗格子演算子に対するRunge-Kutta法の係数最適化とその高速化"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"数値解析","subitem_subject_scheme":"Other"}]},"item_type_id":"4","publish_date":"2022-07-20","item_4_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"東京大学"},{"subitem_text_value":"東京大学"},{"subitem_text_value":"University of Wuppertal"},{"subitem_text_value":"工学院大学"}]},"item_4_text_4":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_value":"The University of Tokyo","subitem_text_language":"en"},{"subitem_text_value":"The University of Tokyo","subitem_text_language":"en"},{"subitem_text_value":"University of Wuppertal","subitem_text_language":"en"},{"subitem_text_value":"Kogakuin University","subitem_text_language":"en"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_publisher":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"情報処理学会","subitem_publisher_language":"ja"}]},"publish_status":"0","weko_shared_id":-1,"item_file_price":{"attribute_name":"Billing file","attribute_type":"file","attribute_value_mlt":[{"url":{"url":"https://ipsj.ixsq.nii.ac.jp/record/218945/files/IPSJ-HPC22185007.pdf","label":"IPSJ-HPC22185007.pdf"},"date":[{"dateType":"Available","dateValue":"2024-07-20"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-HPC22185007.pdf","filesize":[{"value":"1.3 MB"}],"mimetype":"application/pdf","priceinfo":[{"tax":["include_tax"],"price":"660","billingrole":"5"},{"tax":["include_tax"],"price":"330","billingrole":"6"},{"tax":["include_tax"],"price":"0","billingrole":"14"},{"tax":["include_tax"],"price":"0","billingrole":"44"}],"accessrole":"open_date","version_id":"3b972d43-e65a-449d-9908-a530b3ec4814","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2022 by the Information Processing Society of Japan"}]},"item_4_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"依田, 凌"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"中島, 研吾"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Matthias, Bolten"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"藤井, 昭宏"}],"nameIdentifiers":[{}]}]},"item_4_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AN10463942","subitem_source_identifier_type":"NCID"}]},"item_4_textarea_12":{"attribute_name":"Notice","attribute_value_mlt":[{"subitem_textarea_value":"SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc."}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourceuri":"http://purl.org/coar/resource_type/c_18gh","resourcetype":"technical report"}]},"item_4_source_id_11":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"2188-8841","subitem_source_identifier_type":"ISSN"}]},"item_4_description_7":{"attribute_name":"論文抄録","attribute_value_mlt":[{"subitem_description":"近年の大型計算機の超並列構成により，時間発展偏微分方程式 (time-dependent PDEs) の数値解法として Multigrid 法に基づく時間並列解法，特に Multigrid Reduction in Time (MGRIT) が注目されている．MGRIT は放物型 PDE に対して多数の成功例が報告されている一方で，双曲型 PDE に対しては収束性の悪化や発散が問題となっている．近年，この収束性悪化は拡大した時間刻み幅を用いる再離散化により構築される粗格子演算子に起因することが明らかになり，適切な粗格子演算子を効率的に構築することが課題となっている．本研究では粗いレベルにおいて Runge-Kutta 法による時間積分を仮定し，Butcher 配列の段数と係数を最適化することで MGRIT の収束性向上を図る．また段数増加に伴う粗いレベルのコスト増加を削減するために，時間方向の粗格子集約に基づく空間再分散法を併用し，収束性とスケーラビリティの双方の改善を検討する．周期境界条件における一次元線形移流方程式を対象とした数値実験では，再離散化では発散し収束しない問題に対して，最適化により収束を達成する多段 0 次精度スキームが確認された．このスキームを粗いレベルで用いた MGRIT の振る舞いを収束性解析とスケーリングの評価実験も含めて報告する．","subitem_description_type":"Other"}]},"item_4_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"11","bibliographic_titles":[{"bibliographic_title":"研究報告ハイパフォーマンスコンピューティング（HPC）"}],"bibliographicPageStart":"1","bibliographicIssueDates":{"bibliographicIssueDate":"2022-07-20","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"7","bibliographicVolumeNumber":"2022-HPC-185"}]},"relation_version_is_last":true,"weko_creator_id":"44499"},"id":218945,"links":{}}