A numerical eigenvalue study of preconditioned non-equilibrium transport equations

The finite element integration of non-equilibrium contaminant transport in porous media yields sparse, unsymmetric, real or complex equations, which m ay be solved by iterative projection methods, such as Bi-CGSTAB and TFQMR, on condition that they are effectively preconditioned. To ensure a fast con vergence, the eigenspectrum of the preconditioned equations has to be very compact around unity. Compactness is generally measured by the spectral con dition number. In difficult advection-dominated problems, however, the cond ition number may be large and nevertheless, convergence may be good. A nume rical study of the preconditioned eigenspectrum of a representative test ca se is performed using the incomplete triangular factorization. The results show that preconditioning eliminates most of the original complex eigenvalu es, and that compactness is not necessarily jeopardized by a large conditio n number. Quite surprisingly, it is shown that the preconditioned complex p roblem may have a more compact real eigenspectrum than the equivalent real problem. Copyright (C) 1999 John Wiley & Sons, Ltd.