Improving the convergence rate to steady state of parabolic ADI methods

The present, residuals' L(2)-norms analysis of the rate of convergence to steady state for parabolic ADI solvers allows the prediction of the number of iterations required for convergence, as a function of the Courant number alpha. A modification of current ADI codes is presented which significantly improves the convergence rate and is insensitive to the Courant number over a large range of alpha. This corrected algorithm is tested for the cases of Dirichlet problems for uniform grids of many mesh sizes, mixed Dirichlet-Neumann problems, and problems defined on stretched grids and/or problems with variable coefficients.