AN ADAPTIVE MULTIGRID SOLVER FOR PLATE VIBRATION AND BUCKLING PROBLEMS

The paper describes a finite element multigrid strategy for the;soluti on of plate vibration and buckling problems. The solution procedure co mbines the residual iteration scheme used in Casciaro R, Aristodemo M. International Conference on Finite Elements Nonlinear Solid and Struc tural Mechanics, Gelio, Norway, 1977, (main loop) with the adaptive mu ltigrid scheme proposed in Lopez S, Casciaro R. International Journal of Numerical methods in Engineering 1997,40:919-96. A subspace iterati on technique allows several principal eigensolutions to be obtained si multaneously. The sequence of meshes used by the multigrid process is generated through an adaptive local refinement based on the Zienkiewic z-Zhu estimate of the discretization error Zienkiewicz OC, Zhu JZ. Int ernational 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 effec tiveness of the algorithm. (C) 1998 Elsevier Science Ltd. All rights r eserved.