###### Abstract  
In this article, a newly developed multiple-source meshless method (MSMM) capable of solving inverse heat conduction problems in two dimensions is presented. Evolved from the collocation Trefftz method (CTM), the MSMM approximates the solution by using many source points through the addition theorem such that the ill-posedness is greatly reduced. The MSMM has the same superiorities as the CTM, such as the boundary discretization only, and is advantageous for solving inverse problems. Several numerical examples are conducted to validate the accuracy of solving inverse heat conduction problems using boundary conditions with different levels of noise. Moreover, the domain decomposition method is adopted for problems in the doubly-connected domain. The results demonstrate that the proposed method may recover the unknown data with remarkably high accuracy, even though the over-specified boundary data are assigned a portion that is less than 1/10 of the overall domain boundary. m m  
method (GFDM) to recover the heat source for steady-state heat conduction problems. For the inverse problem, the boundary condition is only given for portions of the domain boundary, and the given boundary data often include different levels of noise in which the problem is usually a severely ill-posed problem. To deal with inverse problems, several numerical techniques have been proposed to improve the ill-conditioning matrix. In 2005, [PERSON] et al. [10] utilized the MFS in cooperation with the exponentially convergent scalar homotopy algorithm (ECSHA) to treat the ill-posed phenomenon for the inverse Cauchy problem. [PERSON] [11] presented the mixed formulation of quasi-reversibility to solve the Cauchy problem for the Laplace governing equation. In order to use this technique, the numerical results can be carried out easily without using the iterative method. Later, [PERSON], [PERSON], and [PERSON] introduced [12] an approach based on the minimization of an energy error functional for temperature and heat flux data recovering. The Tikhonov regularization technique [13; 14] is one of the commonly used methods to mitigate the ill-posed phenomenon. Moreover, the L-curve method [15; 16] is often found to obtain the regularization parameter. In the past decades, mesh-based numerical methods have been commonly used to solve the inverse problem, such as the finite difference method [17; 18] and the boundary element method [19; 20]. However, the development of new numerical methods has still attracted interests. The meshless approach may be one of the most competitive alternatives recently. Among the meshless methods, such as the collocation Trefftz method (CTM) [21; 22], the MFS [23], boundary knot method [24], element-free Galerkin method [25], radial basis function collocation method [26], multi-scale polynomial expansion method [27], and boundary particle method [28], the boundary-type meshless method is perhaps the most simple and accurate method. The CTM and the MFS are based on the Trefftz method, in which the CTM adopts T-complete functions and the MFS includes the fundamental solution as the basis functions. Since the T-complete functions and the fundamental solution are solutions of the governing equation, the boundary points may only need to be placed on the domain boundary. The CTM and MFS are therefore referred to boundary-type meshless methods, which usually suffer from the numerical instability due to the ill-posed phenomenon of the meshless method. To improve the applicability of the CTM and MFS, [PERSON] et al. [29; 30] propose the multiple source meshless method (MSMM). The newly developed MSMM is modified from the CTM and MFS and combines the benefits of both methods. The MSMM resolves the problem of finding proper locations of source points in the MFS and reduces the ill-posed problem from higher order Trefftz terms in the CTM. Consequently, the MSMM can be a promising method for solving inverse heat conduction problems.