Improving the convergence rate of parabolic ADI methods

The rate of convergence to steady state of parabolic Alternating Direction Implicit (ADI) solvers is analyzed in terms of the L(2)-norms of the residuals. The analysis allows one to predict the number of iterations necessary for convergence as function of the Courant number, Lambda. A simple modification of existing ADI codes is devised. It improves the convergence rate substantially and is insensitive to the Courant number in a large range of Lambda.