Convergence characteristics of approximate factorization methods

Convergence characteristics and efficiency of several implicit approximate factorization schemes (including standard ADI, a diagonally dominant form of ADI:DDADI and a diagonalized version of DDADI:D3ADI) are examined using stability analysis and numerical convergence studies. We also discuss the use of subiterations to eliminate the approximate factorization errors and thereby improve convergence behavior. Numerical convergence studies are utilized to demonstrate the theoretical findings. We conclude that, ADI and D3ADI with sub-iterations perform equally well in terms of efficiency, although D3ADI may be more robust with respect to time step selection.