Comparative Study of Chebyshev Acceleration and Residue Smoothing in the Solution of Nonlinear Elliptic Difference Equations

摘要

Chebyshev acceleration is compared with an acceleration technique based on residue smoothing. The effect of residue smoothing is that the spectral radius of the Jacobian matrix associated with the system of equations can be reduced substantially, so that the eigenvalues of the iteration matrix of the iteration method used are considerably decreased. Comparative experiments clearly indicate that residue smoothing is superior to Chebyshev acceleration. A model problem shows that the rate of convergence of the smoothed Jacobi process is comparable with that of ADI methods. The smoothing matrices by which the residue smoothing is achieved allow for a very efficient implementation, thus hardly increasing the computational effort of the iteration process. Residue smoothing is directly applicable to nonlinear problems without affecting the algorithmic complexity. The simplicity of the method offers excellent prospects for execution on vector and parallel computers.