Research on the Recognition Algorithm concerning Geometric Boundary regarding Heat Conduction Based on BEM and CGM

An inverse algorithm on boundary element method and conjugate gradient method is proposed to solve the problem of thermal conduction inverse of geometric shape. The direct problem is solved with the boundary element method, while the solution to the inverse problem is obtained through optimizing the objective function in the conjugate gradient method. Taking into account the identification of different material specimens when the unknown boundary is sinusoidal, step function, or circular shape, the influence of initial value, temperature error, thermal conductivity, and thermal intensity on the precision of inversion solution is discussed. The experimental results show that the method can recognize various irregular boundaries and is insensitive to initial values, measurement errors, and heat intensity. The thermal conductivity has a certain effect on this method. The inversion accuracy is higher on the condition that the thermal conductivity is smaller.