Meshless Method for Geometry Boundary Identification Problem of Heat Conduction

Abstract

A geometry identification problem of two-dimensional heat conduction is solved by using the least-squares collocation meshless method and the conjugate gradient method. In the least-squares collocation meshless approach for solving the direct heat conduction problem, a number of collocation points and auxiliary points are used to discretize the problem domain, and the collocation points are taken to construct the trial function by moving least-squares approximation. Akima cubic interpolation is employed to transform the geometry boundary inverse problem to the discrete boundary point's inverse problem and approximate the unknown boundary in an inverse iterative process. In order to illustrate the performance and verify the new solution method, four typical cases are considered. The numerical results show that the least-squares collocation meshless method combined with the conjugate gradient method is accurate and stable for solving the geometry identification problem of heat conduction.