An Adaptive Multigrid Solver for Plate Vibration and Buckling Problems

Abstract

The paper describes a finite element multigrid strategy for the solution of plate vibration and buckling problems. The solution procedure combines the residual iteration scheme used in Casciaro R, Aristodemo M. International Conference on Finite Elements Nonlinear Solid and Structural Mechanics, Gelio, Norway, 1977, (main loop) with the adaptive multigrid scheme proposed in Lopez S, Casciaro R. International Journal of Numerical methods in Engineering 1997;40:919–96. A subspace iteration technique allows several principal eigensolutions to be obtained simultaneously. The sequence of meshes used by the multigrid process is generated through an adaptive local refinement based on the Zienkiewicz–Zhu estimate of the discretization error Zienkiewicz OC, Zhu JZ. International Journal of Numerical Methods in Engineering 1987;24:337–57. A pointer-based data structure and an HC Aristoderno M. Computers and Structures 1985;21(5):987–93, finite element discretization make the solution process highly efficient. Some numerical tests show the effectiveness of the algorithm.