MULTILEVEL AGGREGATION METHOD FOR SOLVING LARGE-SCALE GENERALIZED EIGENVALUE PROBLEMS IN STRUCTURAL DYNAMICS

✍ Scribed by V. E. BULGAKOV; M. V. BELYI; K. M. MATHISEN

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 415 KB
• Volume: 40
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19970215)40:3<453::aid-nme74>3.0.co;2-2

✦ Synopsis

In this paper a novel iterative method of multilevel type for solving large-scale generalized eigenvalue problems encountered in structural dynamics is presented. A preconditioned iterative technique, which can be viewed as a modification of the Subspace Iteration method, is used for simultaneous calculation of a group of lowest modes and frequencies. The paper demonstrates that a coarse aggregation model can be employed in the hierarchical structure of the preconditioner in order to provide a good resemblance of the latter to the stiffness matrix of the finite element approximation with respect to low-frequency modes. This leads to a fast convergent procedure of subspace iterations. As opposed to the coarse grid used in methods of multigrid type, this model allows for solving problems with different finite elements including reticulated structures in the framework of large comprehensive finite element software systems. Numerical experiments performed for three-dimensional truss, frame and solid structures demonstrate an excellent performance of the method.