Reducing Data Size Inequality during Finite Element Model Separation into Superelements

• Main Authors: Yu. V. Berchun, I. A. Kiselev, M. M. Biryukova, S. S. Sokolov, A. S. Shevchenko
• Format: Article
• Language: Russian
• Published: MGTU im. N.È. Baumana 2015-01-01
• Series: Nauka i Obrazovanie
• Subjects: finite element method; superelement method; separation into superelements; superelements forming; data size
• Online Access: http://technomag.edu.ru/jour/article/view/888

The work considers two methods of automatic separation of final element model into super-elements to decrease computing resource demand when solving the linearly - elastic problems of solid mechanics. The first method represents an algorithm to separate a final element grid into simply connected sub-regions according to the set specific number of nodes in the super-element. The second method is based on the generation of a super-element with the set specific data size of the coefficient matrix of the system of equations of the internal nodes balance, which are eliminated during super-element transformation. Both methods are based on the theory of graphs. The data size of a matrix of coefficients is assessed on the assumption that the further solution of a task will use Holetsky’s method. Before assessment of data size, a KatkhillaMackey's (Cuthill-McKee) algorithm renumbers the internal nodes of a super-element both to decrease a profile width of the appropriate matrix of the system of equations of balance and to reduce the number of nonzero elements. Test examples show work results of abovementioned methods compared in terms of inequality of generated super-element separation according to the number of nodes and data size of the coefficient matrix of the system of equations of the internal nodes balance. It is shown that the offered approach provides smaller inequality of data size of super-element matrixes, with slightly increasing inequality by the number of tops.