Efficient Group Iterative Method for Solving the Biharmonic Equation

The biharmonic equations arise in many applications such as elasticity, fluid mechanics, and many other areas. In this paper, the combination of Explicit Decoupled Group (EDG) method with Successive Over Relaxation (SOR) is proposed for solving the biharmonic equation by reducing this equation into a coupled second order Poisson equations. Thus, this pair of Poisson equations can be easily solved using finite difference method, which discretizes the solution domain into a finite number of grids. The sparse linear system derived is usually solved by iterative methods which always take advantage of the existence of zeros in the coefficient matrix. However, such methods yield high number of iterations for convergence especially if the number of grid points is very large. To overcome of this problem, EDG SOR method formulated to accelerate the rate of convergence for the solution of these iterative methods. The numerical experiments carried out confirm the superiority of the introduced method over the classical standard five point SOR formula in terms of number of iterations and execution time.