Multilevel preconditioners for a quadrature Galerkin solution of a biharmonic problem

Efficient numerical algorithms are developed and analyzed that implementmultilevel preconditioners for the solution of the quadrature finite element Galerkin approximation of the biharmonic Dirichlet problem. The quadrature scheme is formulated using the Bogner-Fox-Schmit rectangular element and the product two-point Gaussian quadrature. The proposed additive and multiplicative preconditioners are uniformly spectrally equivalent to the operator of the quadrature scheme. Implemented by optimal cost algorithms, the preconditioners are applied to accelerate convergence of the preconditioned conjugate gradient algorithm. Numerical results are presented that demonstrate the efficiency of the preconditioners. c © John Wiley & Sons, Inc.