In this paper, Laplace transform triple reciprocity boundary element method (LT-TRBEM) is employed to solve the three dimensional transient heat conduction problems. In order to improve the accuracy of the Laplace inversion using Gaver-Wynn-Rho (GWR) algorithm in non-multi-precision computational environment, a precision controllable GWR (PCGWR) algorithm is proposed in the current study. The inversion parameter N_L will be selected automatically according to inverse transform accuracy. Solutions with very poor precision in GWR will be identified and eliminated by PCGWR to guarantee the inverse transform accuracy. In LT-TRBEM, there is a non-integral term containing fundamental solution in the boundary integral equation (BIE) for domain points. The value of it is infinite and cannot be calculated directly. In order to supplement this shortcoming, a computable BIE for domain points is proposed, the term with infinite value is converted into a known amount of boundary integral. So, we can calculate the domain points’ temperature successfully, and LT-TRBEM can be employed in problems with discontinuous boundary conditions. Three numerical examples were included to demonstrate the performance of the proposed approach. In summary, LT-TRBEM combined with the PCGWR and the new BIE for domain points can capture the transient heat conduction responses efficiently and accurately.

本文采用拉普拉斯变换三重互易边界元方法（LT-TRBEM）解决了三维瞬态导热问题。为了提高在非多精度计算环境中使用Gaver-Wynn-Rho（GWR）算法进行拉普拉斯反演的准确性，提出了一种精密可控GWR（PCGWR）算法。反演参数N _L将根据逆变换精度自动选择。PCGWR将识别并消除GWR精度极差的解决方案，以确保逆变换精度。在LT-TRBEM中，在域积分的边界积分方程（BIE）中有一个包含基础解的非积分项。它的值是无限的，不能直接计算。为了弥补这一缺点，提出了一种针对域点的可计算BIE，将具有无限值的项转换为已知量的边界积分。因此，我们可以成功计算出域点的温度，并且LT-TRBEM可以用于边界条件不连续的问题。包括三个数值示例，以证明所提出方法的性能。综上所述，