An Efficient Implementation of Coupling and Decoupling Scheme for Biharmonic Equation

Document Type : Original Article

Authors

1 Department of Basic Engineering Sciences, Faculty of Engineering at Benha, Benha University, Benha, Egypt.

2 Department of Basic Science, The British University in Egypt, Cairo, Egypt.

Abstract

A method for coupling and decoupling, utilizing finite difference, is developed to solve the biharmonic problem on a unit square. This problem is reformulated as a coupled system involving two second-order partial differential equations. This approach necessitates solving the original problem through a sequence of boundary value problems for the Poisson equation. It achieves this using a minimal number of mesh points, distinguishing itself from the traditional methods employed in prior research to address this particular issue. A compact finite difference scheme has been introduced for the solution of fourth and sixth-order Poisson equations. This innovative approach effectively reduces the computational cost of the proposed algorithm, especially when dealing with large grid numbers, compared to traditional methods. Simultaneously solving these Poisson equations can be easily programmed. We plan to apply this method to analyze the fourth-order differential problem of a square clamped plate subjected to various loads. The biharmonic problem has been examined with a focus on achieving higher-order accuracy. The outcomes of numerical experiments showcase the method's optimal global accuracy and reveal super convergence results. Notably, a sixth-order accuracy is observed at both the boundary nodes and interior points.

Files

Share

How to cite

Statistics