Substructuring and Conditioning

In the numerical solution of any mathematical problem, the question of accuracy always arises. When a large system of equations is solved, no exact solution is usually available for making comparisons. Although various tests can be performed on the computed solution, these tests represent necessary rather than sufficient conditions. Thus, a computed solution can satisfy all the necessary conditions but be severely inaccurate. A problem that yields this type of solution is called ill-conditioned. Substructuring is a popular technique for solving certain types of structural problems. It has been suggested that by the judicious choice of substructures some conditioning problems might be alleviated. A numerical investigation was performed to evaluate this suggestion. The results indicate that substructuring does not significantly influence the solution accuracy of ill-conditioned systems.