Collocation methods: More efficient procedures for applying collocation |
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| Affiliation: | 1. School of Civil Engineering and Architecture, Linyi University, Linyi, Shandong 276000, China;2. Linyi City Key Lab of Appraisement and Strengthening in Building Structures, Linyi, Shandong 276000, China;3. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China;4. Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing 100124, China;5. School of Civil and Architecture Engineering, Anyang Institute of Technology, Anyang 455000, China;1. Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran;2. Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran;1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China;2. University of Chinese Academy of Sciences, Beijing, 100049, China |
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| Abstract: | In recent years, new and more effective procedures for applying collocation have been published. This article is devoted to present a revision of this subject and complement its developments. From the general theory two broad approaches are derived, which yield the direct and the indirect TH-collocation methods. The former approach had not been published before, and it is a dual of the indirect approach. In particular, second order differential equations of elliptic type are considered and several orthogonal collocation algorithms are developed for them. In TH-collocation, the approximations on the internal boundary and in the subdomain interiors are completely independent. This yields clear computational advantages that are illustrated through the construction of such algorithms. In the implementations presented, three dimensional problems are included. In passing, single-point-collocation methods that have been the subject of several recent publications are revised. |
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