Decomposition Method for Solving the Quadratic Programming Problem in the Aircraft Assembly Modeling

Aircraft assembly modeling requires solving the contact problem which can be reduced to the Quadratic Programming (QP) problem with dense ill-conditioned Hessian. For dozens of thousands of variables solving the QP problem requires huge time and RAM space. This paper suggests decomposing the problem into several sub-QP problems according to the geometric regions to reduce both solving time and memory requirements. The important feature of the considered QP problem is the density of the Hessian matrix which means that decomposed regions have mutual interference not only along their common boundary but instead on their whole areas. Suggested decomposition method solves sub-QP problems iteratively until the solution of the original QP is found. Convergence is proved under certain conditions. The results for test models of fuselage section joint and simultaneous joint of the upper and lower wing panels are presented.