A multiunit ADI scheme for biharmonic equation with accelerated convergence

We consider the problem of acceleration of the Alternative Directions Implicit (ADI) scheme for Dirichlet problem for biharmonic equation. The second Douglas scheme is used as the main vehicle and two full time steps are organised in a single iteration unit in which the explicit operators are arranged differently for the second step. Using an a priori estimate for the spectral radius of the operator, we show that there exists an optimal value for the acceleration parameter. An algorithm is devised implementing the scheme and the optimal range of the parameter is verified through numerical experiments. One iteration unit speeds up the convergence from two to three times in comparison with the standard ADI scheme. To obtain more significant acceleration for the cases when the standard ADI scheme has extremely slow convergence, a generalised multiunit scheme is constructed by introducing another acceleration parameter and treating two consecutive iteration units as one basic element.