On the Accuracy of the Collocation Trefftz Method for Solving Two and Three Dimensional Heat Equations
Cheng-Yu Kua Jing-En Xiaoa Chih-Yu Liua Weichung Yeiha
a Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan
In 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.
Keywords: Trefftz method; Ill-conditioned; Characteristic length; Cylindrical harmonics; Three dimensional
Cheng-Yu Ku*, Jing-En Xiao, Chih-Yu Liu, Weichung Yeih (2016), “On the Accuracy of the Collocation Trefftz Method for Solving Two and Three Dimensional Heat Equations”, Numerical Heat Transfer, Part B: Fundamentals: An International Journal of Computation and Methodology, Volume 69, Issue 4, pp. 334-350, 2016, http://dx.doi.org/10.1080/10407790.2015.1125215. (IF 1.330, SCIE, 30/58, Q2 in THERMODYNAMICS, JCR 2015)
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