In this study, the interpolating element-free Galerkin (IEFG) method for solving three-dimensional (3D) transient heat conduction problem is presented. By using the improved interpolating moving least-squares (IIMLS) method to form the shape function, and using the weak form of 3D transient heat conduction problems to obtain the discretized equations, the formulae of the IEFG method are obtained. The shape function of the IIMLS method satisfies the property of Kronecker delta function, and then the IEFG method can apply essential boundary conditions directly, which can result in higher computational speed and accuracy. Some examples are given to discuss the convergence and advantages of the IEFG method. By analyzing the numerical results obtained by IEFG method and improved EFG method, we conclude that IEFG method has clear advantages in computational speed and accuracy.

在这项研究中，提出了用于解决三维（3D）瞬态热传导问题的无插值Galerkin（IEFG）方法。通过使用改进的插值移动最小二乘（IIMLS）方法来形成形状函数，并使用3D瞬态导热问题的弱形式来获得离散方程，从而获得IEFG方法的公式。IIMLS方法的形状函数满足Kronecker德尔塔函数的性质，然后IEFG方法可以直接应用必要的边界条件，从而可以提高计算速度和准确性。给出了一些实例来讨论IEFG方法的收敛性和优点。通过分析IEFG方法和改进的EFG方法获得的数值结果，