Abstract
ABSTRACTIn this article, we first propose a novel Trefftz energy method (TEM) for the numerical analysis of heat transfer in arbitrary plane domains. The TEM introduces the Trefftz energy bases in the complete linear space to approximate the numerical solution of the mixed boundary value problem in the heat transfer over an arbitrary plane domain. The Trefftz energy bases not only satisfy the Laplace equation but also preserve the energy, whose performance is better than the original Trefftz bases. Three benchmark numerical examples are tested to demonstrate the efficiency and accuracy of the proposed TEM. Although the multiple-scale Trefftz method can treat these problems with high accuracy, the TEM can further raise the accuracy with one order. Therefore, the present scheme is a competitive alternative to existing methods for solving heat transfer problems in arbitrary plane domains.
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