On the accuracy of the collocation Trefftz method for solving two- and three-dimensional heat equations. (2nd April 2016) - Ku, Cheng-Yu; Xiao, Jing-En; Liu, Chih-Yu; Yeih, Weichung
ABSTRACT: In this article, the accuracy of the collocation Trefftz method (CTM) for solving two- and three-dimensional heat equations is investigated. The numerical solutions are approximated by superpositioning T-complete functions formulated using cylindrical harmonics. To avoid the ill-conditioning of the CTM, the characteristic lengths and the multiple-scale Trefftz method are adopted. The results reveal 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.