{"id":1203,"date":"2016-08-12T20:25:07","date_gmt":"2016-08-12T12:25:07","guid":{"rendered":"http:\/\/140.121.146.12\/wordpress\/?p=1203"},"modified":"2016-08-12T20:25:07","modified_gmt":"2016-08-12T12:25:07","slug":"research-article-2","status":"publish","type":"post","link":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/?p=1203","title":{"rendered":"\u914d\u9ede TREFFTZ \u65b9\u6cd5 \u7814\u7a76\u65b0\u77e5"},"content":{"rendered":"<p>\t\t\t\t<![CDATA[On the Accuracy of the Collocation Trefftz Method for Solving Two and Three Dimensional Heat Equations\nCheng-Yu Ku<sup>a<\/sup> Jing-En Xiao<sup>a<\/sup> Chih-Yu Liu<sup>a<\/sup> Weichung Yeih<sup>a<\/sup>\n<em><sup>a<\/sup><\/em><em> Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan <\/em>\n&nbsp;\n<strong>ABSTRACT<\/strong>\nIn this article, the accuracy of the collocation Trefftz method (CTM) for solving two and three dimensional heat equations was investigated. The numerical solutions were approximated by superpositioning T-complete functions formulated using cylindrical harmonics. To avoid the ill-conditioned system of the CTM, the characteristic lengths and the multiple-scale Trefftz method were adopted. The results revealed that for two-dimensional problems, the CTM can provide highly accurate numerical solutions, with the accuracy increasing with the order of the terms. For three-dimensional problems, highly accurate numerical solutions can be obtained using a certain order of terms, where the order is determined by performing an accuracy assessment.\nKeywords: Trefftz method; Ill-conditioned; Characteristic length; Cylindrical harmonics; Three dimensional\n\u5f15\u7528\u6587\u737b\nCheng-Yu Ku*, Jing-En Xiao, Chih-Yu Liu, Weichung Yeih (2016), &#8220;On the Accuracy of the Collocation Trefftz Method for Solving Two and Three Dimensional Heat Equations&#8221;, <em><u>Numerical Heat Transfer, Part B: Fundamentals: An International Journal of Computation and Methodology<\/u><\/em>, <a href=\"http:\/\/www.tandfonline.com\/loi\/unhb20?open=69&amp;repitition=0#vol_69\">Volume 69<\/a>, <a href=\"http:\/\/www.tandfonline.com\/toc\/unhb20\/69\/4\">Issue 4<\/a>, pp. 334-350, 2016, <em><u>http:\/\/dx.doi.org\/10.1080\/10407790.2015.1125215<\/u>.<\/em> (IF 1.330, SCIE, 30\/58, Q2 in THERMODYNAMICS, JCR 2015)\nFull paper link:\nhttps:\/\/drive.google.com\/open?id=0B6KIiA0ONNL1dnE0Ni0xNnh2NEE]]>\t\t<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\t\t\t\t<![CDATA[]]>\t\t<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[9],"class_list":["post-1203","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-uncategorized"],"_links":{"self":[{"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/1203","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1203"}],"version-history":[{"count":0,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/1203\/revisions"}],"wp:attachment":[{"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1203"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1203"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}