Application of the complex variable step method and the boundary element method for sensitivity analysis of steady heat conduction problems

The paper concerns the problems related to applying the complex variable step method for the sensitivity analysis of the steady temperature field in the solid body domain due to the perturbations of the geometrical and physical parameters. The optimization problem using the approach proposed is also discussed. At the stage of numerical modelling, the boundary element method is used. The first part of the paper is devoted to the shape sensitivity. The results obtained are compared with the solution resulting from the implicit approach of sensitivity analysis. In the second part, the practical problem concerning optimizing the geometry of continuous casting mould cross-section is considered. The project variable vector contains the cooling pipes' radius and the volume flow rate of the cooling water. The numerical results and the conclusions are presented in the final part of the paper.