Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
On an Alternating Direction Method for Solving the Plate Problem with Mixed Boundary Conditions
Journal of the ACM (JACM)
Fast finite-difference solution of biharmonic problems
Communications of the ACM
A multiunit ADI scheme for biharmonic equation with accelerated convergence
International Journal of Computational Science and Engineering
Numerical scheme for Swift-Hohenberg equation with strict implementation of lyapunov functional
Mathematical and Computer Modelling: An International Journal
Non-linear waves of the steady natural convection in a vertical fluid layer: A numerical approach
Mathematics and Computers in Simulation
A multiunit ADI scheme for biharmonic equation with accelerated convergence
International Journal of Computational Science and Engineering
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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.