Trefftz,collocation, and other boundary methods—A comparison |
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| Authors: | Zi‐Cai Li Tzon‐Tzer Lu Hung‐Tsai Huang Alexander H‐D Cheng |
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| Institution: | 1. Department of Applied Mathematics and Department of Computer Science and Engineering, National Sun Yat‐sen University, Kaohsiung, Taiwan 80424. National Center for Theoretical Sciences, Taiwan;2. Department of Applied Mathematics, I‐Shou University, Kaohsiung County, Taiwan 840;3. Department of Civil Engineering, University of Mississippi, University, MS 38677PO Box 1848, University of Mississippi, University, MS 38677‐1848 |
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| Abstract: | In this article we survey the Trefftz method (TM), the collocation method (CM), and the collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal conditions, which include the indirect Trefftz method, the original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Other boundary methods are also briefly described. Key issues in these algorithms, including the error analysis, are addressed. New numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm and provides the most accurate solution with the best numerical stability. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 |
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| Keywords: | Trefftz method indirect Trefftz method direct Trefftz method hybrid Trefftz method boundary method boundary elements method boundary integral method |
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