Solving the higher-dimensional nonlinear inverse heat source problems by the superposition of homogenization functions method. (October 2019) - Liu, Chein-Shan; Qiu, Lin; Lin, Ji
Highlights: A novel scheme is developed to address the nonlinear inverse heat source problems. The proposed method does not need iteration to solve nonlinear equations. The presented method is quite accurate, effective and robust. Abstract: The paper solves the higher-dimensional inverse heat source problems of nonlinear convection-diffusion-reaction equations in 2D rectangles and 3D cuboids, of which the final time data and the Neumann boundary data on one-side are over-specified. Firstly, we derive a family of single-parameter space-time homogenization functions. Secondly, the temperature is obtained through the superposition of the homogenization functions and solving a linear system to satisfy the over-specified Neumann boundary condition. Thirdly, the unknown heat source is recovered by the back substitution of the numerical solution of temperature into the nonlinear governing equation. Numerical tests reveal that the novel method is very accurate to find the solution and to recover the unknown space-time dependent heat source function in the whole space–time domain, whose required extra data are very saving.