An Operator Splitting Scheme for Biharmonic Equation with Accelerated Convergence
We consider the acceleration of operator splitting schemes for Dirichlet problem for biharmonic equation. The two fractional steps are organized in a single iteration unit where 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 which speeds up the convergence from two to three times. An algorithm is devised implementing the scheme and the optimal range is verified through numerical experiments.
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- 2.Bodewig, E.: Matrix Calculus 4. Interscience Publishers Inc., New York (1956)Google Scholar
- 4.Christov, C.I., Ridha, A.: Splitting scheme for iterative solution of biharmonic equation. Application to 2D Navier-Stokes problems. In: Dimov, I., Sendov, B.l., Vasilevski, P. (eds.) Advances in Numerical Methods and Applications, pp. 341–352. World Scientific, Singapore (1994)Google Scholar