Inverse heat conduction problem with a nonlinear source term by a local strong form of meshless technique based on radial point interpolation method

This study is devoted to find the numerical solution of the surface heat flux history and temperature distribution in a non linear source term inverse heat conduction problem (IHCP). This type of inverse problem is investigated either with a temperature over specification condition at a specific point or with an energy over specification condition over the computational domain. A combination of the meshless local radial point interpolation and the finite difference method are used to solve the IHCP. The proposed method does not require any mesh generation and since this method is local at each time step, a system with a sparse coefficient matrix is solved. Hence, the computational cost will be much low. This non linear inverse problem has a unique solution, but it is still ill-posed since small errors in the input data cause large errors in the output solution. Consequently, when the input data is contaminated with noise, we use the Tikhonov regularization method in order to obtain a stable solution. Three different kinds of schemes are applied to choose the regularization parameter which are in agreement with each other. Numerical results show that the solution is accurate for exact data and stable for noisy data.