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首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >On the accuracy of the collocation Trefftz method for solving two- and three-dimensional heat equations
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On the accuracy of the collocation Trefftz method for solving two- and three-dimensional heat equations

机译：搭配Trefftz方法求解二维和三维热方程的准确性

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摘要

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.
机译：在本文中，研究了搭配Trefftz方法（CTM）求解二维和三维热方程的准确性。通过叠加使用圆柱谐波公式化的T-完全函数来近似数值解。为避免CTM出现问题，采用了特征长度和多尺度Trefftz方法。结果表明，对于二维问题，CTM可以提供高度精确的数值解，并且精度会按术语的顺序增加。对于三维问题，可以使用某些项的顺序来获得高度精确的数值解，其中该顺序通过执行准确性评估来确定。

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