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 may be solved by iterative projection methods, such as Bi-CGSTAB and TFQMR, on condition that they are effectively preconditioned. To ensure a fast convergence, the eigenspectrum of the preconditioned equations has to be very compact around unity. Compactness is generally measured by the spectral condition number. In difficult advection-dominated problems, however, the condition number may be large and nevertheless, convergence may be good. A numerical study of the preconditioned eigenspectrum of a representative test case is performed using the incomplete triangular factorization. The results show that preconditioning eliminates most of the original complex eigenvalues, and that compactness is not necessarily jeopardized by a large condition number. Quite surprisingly, it is shown that the preconditioned complex problem may have a more compact real eigenspectrum than the equivalent real problem. Copyright (C) 1999 John Wiley & Sons, Ltd.
non-equilibrium transport finite elements projection methods non-symmetric eigenproblem