{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T13:13:51Z","timestamp":1743081231998,"version":"3.40.3"},"publisher-location":"Cham","reference-count":17,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030670764"},{"type":"electronic","value":"9783030670771"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-67077-1_3","type":"book-chapter","created":{"date-parts":[[2021,1,7]],"date-time":"2021-01-07T08:41:47Z","timestamp":1610008907000},"page":"39-59","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Complexity Analysis of a Fast Directional Matrix-Vector Multiplication"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2258-7001","authenticated-orcid":false,"given":"G\u00fcnther","family":"Of","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7750-8561","authenticated-orcid":false,"given":"Raphael","family":"Watschinger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,1,8]]},"reference":[{"issue":"1","key":"3_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00211-014-0656-7","volume":"130","author":"M Bebendorf","year":"2015","unstructured":"Bebendorf, M., Kuske, C., Venn, R.: Wideband nested cross approximation for Helmholtz problems. Numer. Math. 130(1), 1\u201334 (2015). https:\/\/doi.org\/10.1007\/s00211-014-0656-7","journal-title":"Numer. Math."},{"issue":"1","key":"3_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00607-002-1469-6","volume":"70","author":"M Bebendorf","year":"2003","unstructured":"Bebendorf, M., Rjasanow, S.: Adaptive low-rank approximation of collocation matrices. Computing 70(1), 1\u201324 (2003). https:\/\/doi.org\/10.1007\/s00607-002-1469-6","journal-title":"Computing"},{"issue":"6","key":"3_CR3","doi-asserted-by":"publisher","first-page":"e2112","DOI":"10.1002\/nla.2112","volume":"24","author":"S B\u00f6rm","year":"2017","unstructured":"B\u00f6rm, S.: Directional $$\\cal{H}^2$$-matrix compression for high-frequency problems. Numer. Linear. Algebra. Appl. 24(6), e2112 (2017). https:\/\/doi.org\/10.1002\/nla.2112","journal-title":"Numer. Linear. Algebra. Appl."},{"issue":"4","key":"3_CR4","doi-asserted-by":"publisher","first-page":"1704","DOI":"10.1137\/19M124280X","volume":"41","author":"S B\u00f6rm","year":"2020","unstructured":"B\u00f6rm, S., B\u00f6rst, C.: Hybrid matrix compression for high-frequency problems. SIAM J. Matrix Anal. Appl. 41(4), 1704\u20131725 (2020). https:\/\/doi.org\/10.1137\/19M124280X","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"1","key":"3_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00211-017-0873-y","volume":"137","author":"S B\u00f6rm","year":"2017","unstructured":"B\u00f6rm, S., Melenk, J.M.: Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis. Numer. Math. 137(1), 1\u201334 (2017). https:\/\/doi.org\/10.1007\/s00211-017-0873-y","journal-title":"Numer. Math."},{"issue":"1","key":"3_CR6","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/0010-4655(91)90151-A","volume":"65","author":"A Brandt","year":"1991","unstructured":"Brandt, A.: Multilevel computations of integral transforms and particle interactions with oscillatory kernels. Comput. Phys. Commun. 65(1), 24\u201338 (1991). https:\/\/doi.org\/10.1016\/0010-4655(91)90151-A","journal-title":"Comput. Phys. Commun."},{"key":"3_CR7","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1016\/j.jcp.2005.12.001","volume":"216","author":"H Cheng","year":"2006","unstructured":"Cheng, H., et al.: A wideband fast multipole method for the Helmholtz equation in three dimensions. J. Comput. Phys. 216, 300\u2013325 (2006). https:\/\/doi.org\/10.1016\/j.jcp.2005.12.001","journal-title":"J. Comput. Phys."},{"issue":"1","key":"3_CR8","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1016\/j.jcp.2003.12.002","volume":"197","author":"E Darve","year":"2004","unstructured":"Darve, E., Hav\u00e9, P.: Efficient fast multipole method for low-frequency scattering. J. Comput. Phys. 197(1), 341\u2013363 (2004). https:\/\/doi.org\/10.1016\/j.jcp.2003.12.002","journal-title":"J. Comput. Phys."},{"issue":"4","key":"3_CR9","doi-asserted-by":"publisher","first-page":"1710","DOI":"10.1137\/07068583X","volume":"29","author":"B Engquist","year":"2007","unstructured":"Engquist, B., Ying, L.: Fast directional multilevel algorithms for oscillatory kernels. SIAM J. Sci. Comput 29(4), 1710\u20131737 (2007). https:\/\/doi.org\/10.1137\/07068583X","journal-title":"SIAM J. Sci. Comput"},{"issue":"2","key":"3_CR10","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1016\/0021-9991(87)90140-9","volume":"73","author":"L Greengard","year":"1987","unstructured":"Greengard, L., Rokhlin, V.: A fast algorithm for particle simulations. J. Comput. Phys. 73(2), 325\u2013348 (1987). https:\/\/doi.org\/10.1016\/0021-9991(87)90140-9","journal-title":"J. Comput. Phys."},{"key":"3_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-47324-5","volume-title":"Hierarchical matrices: algorithms and analysis, SSCM","author":"W Hackbusch","year":"2015","unstructured":"Hackbusch, W.: Hierarchical matrices: algorithms and analysis, SSCM, vol. 49. Springer, Heidelberg (2015). https:\/\/doi.org\/10.1007\/978-3-662-47324-5"},{"issue":"5","key":"3_CR12","doi-asserted-by":"publisher","first-page":"1028","DOI":"10.1109\/36.921421","volume":"39","author":"B Hu","year":"2001","unstructured":"Hu, B., Chew, W.C.: Fast inhomogeneous plane wave algorithm for scattering from objects above the multilayered medium. IEEE Trans. Geosci. Remote Sens. 39(5), 1028\u20131038 (2001). https:\/\/doi.org\/10.1109\/36.921421","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"issue":"4","key":"3_CR13","doi-asserted-by":"publisher","first-page":"1175","DOI":"10.1016\/j.jcp.2011.09.027","volume":"231","author":"M Messner","year":"2012","unstructured":"Messner, M., Schanz, M., Darve, E.: Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation. J. Comput. Phys. 231(4), 1175\u20131196 (2012). https:\/\/doi.org\/10.1016\/j.jcp.2011.09.027","journal-title":"J. Comput. Phys."},{"issue":"4","key":"3_CR14","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1115\/1.1482087","volume":"55","author":"N Nishimura","year":"2002","unstructured":"Nishimura, N.: Fast multipole accelerated boundary integral equation methods. Appl. Mech. Rev. 55(4), 299\u2013324 (2002). https:\/\/doi.org\/10.1115\/1.1482087","journal-title":"Appl. Mech. Rev."},{"key":"3_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-34042-4","volume-title":"The Fast Solution of Boundary Integral Equations","author":"S Rjasanow","year":"2007","unstructured":"Rjasanow, S., Steinbach, O.: The Fast Solution of Boundary Integral Equations. Springer-Verlag, Berlin, Heidelberg (2007). https:\/\/doi.org\/10.1007\/0-387-34042-4"},{"key":"3_CR16","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1006\/acha.1993.1006","volume":"1","author":"V Rokhlin","year":"1993","unstructured":"Rokhlin, V.: Diagonal forms of translation operators for Helmholtz equation in three dimensions. Appl. Comput. Harmon. A. 1, 82\u201393 (1993). https:\/\/doi.org\/10.1006\/acha.1993.1006","journal-title":"Appl. Comput. Harmon. A."},{"key":"3_CR17","unstructured":"Watschinger, R.: A directional approximation of the Helmholtz kernel and its application to fast matrix-vector multiplications. Master\u2019s thesis, Graz University of Technology, Insitute of Applied Mathematics (2019). https:\/\/permalink.obvsg.at\/AC15364438"}],"container-title":["Lecture Notes in Computer Science","High Performance Computing in Science and Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-67077-1_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,7]],"date-time":"2021-01-07T09:03:12Z","timestamp":1610010192000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-67077-1_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030670764","9783030670771"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-67077-1_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"8 January 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"HPCSE","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on High Performance Computing in Science and Engineering","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Karolinka","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Czech Republic","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"20 May 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23 May 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"hpcse2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/hpcse.it4i.cz\/HPCSE19\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"OCS","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"13","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"9","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"69% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}