{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T22:22:26Z","timestamp":1779315746963,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2016,9,16]],"date-time":"2016-09-16T00:00:00Z","timestamp":1473984000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Basic Research Program of China","doi-asserted-by":"publisher","award":["2011CB013703"],"award-info":[{"award-number":["2011CB013703"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11072052"],"award-info":[{"award-number":["11072052"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51221961"],"award-info":[{"award-number":["51221961"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters in the coastal region, etc. A higher-order scheme is used to discretize geometry of the structure as well as the physical wave potentials. As the kernel of this method, Wehausen\u2019s free-surface Green function is calculated by a newly-developed Gauss\u2013Kronrod adaptive quadrature algorithm after elimination of its Cauchy-type singularities. To improve its computation efficiency, an analytical solution is derived for a fast evaluation of the Green function that needs to be implemented thousands of times. In addition, the OpenMP parallelization technique is applied to the formation of the influence coefficient matrix, significantly reducing the running CPU time. Computations are performed on wave-exciting forces and hydrodynamic coefficients for the long cylindrical structures, either floating or submerged. Comparison with other numerical and analytical methods demonstrates a good performance of the present method.<\/jats:p>","DOI":"10.3390\/computation4030036","type":"journal-article","created":{"date-parts":[[2016,9,19]],"date-time":"2016-09-19T10:07:43Z","timestamp":1474279663000},"page":"36","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["An Extremely Efficient Boundary Element Method for Wave Interaction with Long Cylindrical Structures Based on Free-Surface Green\u2019s Function"],"prefix":"10.3390","volume":"4","author":[{"given":"Yingyi","family":"Liu","sequence":"first","affiliation":[{"name":"Renewable Energy Center, Research Institute for Applied Mechanics, Kyushu University, Kasuga 8168580, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Gou","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Teng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shigeo","family":"Yoshida","sequence":"additional","affiliation":[{"name":"Renewable Energy Center, Research Institute for Applied Mechanics, Kyushu University, Kasuga 8168580, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,9,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1093\/qjmam\/2.2.218","article-title":"On the heaving motion of a circular cylinder on the surface of a fluid","volume":"2","author":"Ursell","year":"1949","journal-title":"Q. 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