Boundary geometry reconstruction for orthotropic heat conduction problems based on HT-FEM

It is usually inconvenient to directly measure the inner boundary geometry shape of thermal pipeline and furnace wall in engineering. A non-iterative algorithm is proposed to reconstruct the geometry shape of these structures for orthotropic heat conduction problems in nondestructive evaluation. First, the temperature of measurement points in the real domain is determined by utilizing the hybrid Trefftz finite element method (HT-FEM). Then, a virtual inner boundary is introduced into forming a virtual domain. The deviation between the measured temperature and the estimated temperature is defined as an objective function. The temperature on the virtual boundary is obtained by calculating the minimum of the objective function. Finally, the virtual boundary temperature is substituted into the direct problem to acquire the temperature distribution in the global domain. And the inner boundary geometry shape is identified by searching the isothermal curve. Several numerical examples are provided to verify the stability and effectiveness of the proposed method. The merit of this algorithm is that the unknown geometry shape can be directly and accurately reconstructed without the complex iterative process.