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A Trefftz method in space and time using exponential basis functions: Application to direct and inverse heat conduction problems

机译：使用指数基函数的时空Trefftz方法：应用于正和反导热问题

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摘要

In this paper we present a Trefftz method based on using exponential basis functions (EBFs) to solve one (1D) and two (2D) dimensional transient problems. We focus on direct and inverse heat conduction problems, the latter being the more challenging ones, to show the capabilities of the method. A summation of exponential basis functions (EBFs), satisfying the governing equation in time and space, with unknown coefficients is considered for the solution. The unknown coefficients are determined by the satisfaction of the prescribed time dependent boundary and initial conditions through a collocation method. Several 1D and 2D direct and inverse heat conduction problems are solved. Some numerical evidence is provided for the convergence and sensitivity of the method with respect to the noise levels of the measured data and time steps.
机译：在本文中，我们提出一种使用指数基函数（EBF）的Trefftz方法来解决一维（1D）和二维（2D）瞬态问题。我们将重点放在直接和反向导热问题上，后者是更具挑战性的问题，以显示该方法的功能。该解决方案考虑了在时间和空间上满足控制方程的指数基函数（EBF）的总和，且系数未知。未知系数是通过搭配方法满足规定的时间依赖性边界和初始条件来确定的。解决了几个一维和二维正向和反向导热问题。对于该方法相对于测量数据和时间步长的噪声水平的收敛性和敏感性，提供了一些数值证据。

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