Collection of abstracts 13th GAMM-Seminar Kiel on Numerical Treatment of Multi-Scale Problems January 24th to 26th, 1997.

Friday, January 24th, 1997

Application of the multi-level aggregation method to structural analysis problems

Recently developed multi-level aggregation method is a method of multigrid type. It is applicable to finite element structural analysis problems ranging from the boundary value theory of elasticity to reticulated frame and truss problems. A special coarsening strategy based on the rigid body motion concept is employed which allows the use of arbitrary displacement formulated finite element model. The hierarchy of aggregation levels is constructed automatically on the basis of information obtained from the finite element stiffness matrix coefficients. The general algebraic scheme of the method consists of the external iterative procedure with multi-level preconditioning. The method has been implemented as an industrial equation solver FEAGS which can be used in large comprehensive finite element software packages. Numerical experiments and industrial computations show that its convergence and solution time in many cases are far superior to modified ICCG and direct methods. Such numerical examples as off-shore platforms, fly wheels, high-rise buildings, gravity dam structures, bus frame and others demonstrate efficiency of the solver.