روش هاي گراف تيوريكي و گراف تيوريكي براي بهينه يابي تربيت در مدلهاي اجزاء محدود

For large-scale structures, the pattern of structural matrices are of great importance. Improving the patterns of sparse matrices not only reduces the cost of solution, but also makes the processing of large matrices feasible. In the present paper, concepts and definitions from graphs and algebraic graph theory are briefly presented Various methods are investigated for optimal ordering to reduce the profile of the structural matrices. Special attention is paid to Sloanʹs method as a powerful approach for profile reduction. In order to show the capability of this method, examples of Everstine are examined. Different values are adopted for the priority function of Sloan and the results are compared. Three parameters are used in place of two, and the resulting profiles are compared. The uniformaty and non-uniformaty of nodal degrees in various models are also studied. The spectral method using the Laplacian matrix of the models is programmed and applied to Everstineʹs examples. The difficulty of computational time is reduced employing improved hybrid spectral-graph method. Combining the hybrid Ritz method and Sloanʹs approach, an improved hybrid Ritz method is developed.