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.
Highlights
The inverse heat conduction problem is the process of computing the unknown temperatures by using over-specified data
Qian, Fu, and Li [8] adopted the method of fundamental solutions (MFS) in conjunction with two different regularization methods for solving the Cauchy problem governed by Laplace equation
We present a newly developed multiple-source meshless method (MSMM) for solving the two-dimensional inverse heat conduction problems
Summary
Featured Application: The inverse heat conduction problems are often encountered in many engineering fields. The temperature can be measured only on a portion of the problem boundary. The information of the remaining boundary is unknown. We develop the multiple-source meshless method to solve the inverse heat conduction problems. The proposed method can be applied on problems in the doubly-connected domain 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
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