Boundary condition identification for oethotropic heat conduction problems based on hybrid Trefftz finite element method without iteration

It is essential to accurately identify the boundary condition of pipeline?s inner wall in engineering analysis and calculation. An efficient non-iterative algorithm based on the hybrid Trefftz finite element method (HT-FEM) is presented to determine the boundary condition of the inner wall for orthotropic media heat conduction problems. The temperature of measurement points is obtained by solving the forward heat conduction problems using the HT-FEM to simulate the experimentally measured data. The evaluated temperature at these points can be formulated as a function of the temperature of the inner boundary nodes, whose boundary conditions remain to be determined. The objective function is established to quantify the deviation between the measured and evaluated temperature at measurement points by utilizing the least-squares approach. The unknown inner boundary conditions are determined by minimizing objective function. Four numerical examples are provided to analyze the inversion results for different types of pipes. The effects of various factors, encompassing the number and location of measurement point, measurement errors, and mixed boundary conditions on inversion results are discussed. The findings demonstrate that the proposed algorithm exhibits high computational efficiency and accuracy in identifying boundary conditions.