A robust incomplete Choleski‐conjugate gradient algorithm

Ajiz, Manzur Ali; Jennings, A.

doi:10.1002/nme.1620200511

Cited by 217 publications

(102 citation statements)

References 10 publications

Supporting

Mentioning

100

Contrasting

Unclassified

Order By: Relevance

“…The linearization of the system is performed by using the Picard method. At each Picard iteration, the resulting set of linear equations is solved by applying a robust Incomplete Choleski Conjugate Gradient algorithm (Ajiz and Jennings, 1984, Axelson and Barker, 1984and Barret et al, 1998. Time step size is determined in an adaptive way, depending on the convergence rate.…”

Section: Numerical Modelmentioning

confidence: 99%

Saltwater Upconing and Decay Beneath a Well Pumping Above an Interface Zone

2005

View full text Add to dashboard Cite

Saltwater, or brine, underlies fresh water in many aquifers, with a transition zone separating them. Pumping fresh water by wells located above the transition zone produces upconing of the latter, eventually salinizing the pumped water, forcing shut-off. The salinity of the pumped water depends on the pumping rate, on the location of the well's screen, on the fresh water flow regime, and on the difference in density between fresh and salt water, expressed as a dimensionless factor called density difference factor (DDF). Following the well's shut-off, the upconed saltwater mound undergoes decay, tending to return to the prepumping regime. In this paper, the upconing-decay processes in an axially symmetrical system are investigated to discover how they are affected by the DDF and by the dispersivities. The code FEAS-Brine, developed for the simulation of coupled density-dependent flow and salt transport, is used. In this code, the flow equation is solved by the Galerkin finite element method (FEM), while the advective-dispersive salt transport equation is solved in the EulerianLagrangian framework. This code does not suffer from the instability constraint on the Peclet number in the vicinity of the pumping well, where advection dominates the salt transport. Simulation results show that upconing is very sensitive to the DDF, which, in our work, is in the range from 0 (for ideal tracer) to 0.2 (for brine). It is shown that for the DDF of 0.025 (for seawater), local upconing occurs only for low iso-salinity surfaces, while those of high salt concentration, practically, do not shift toward the pumping well. For an ideal tracer, all isosalinity surfaces rise toward the pumping well. For brine, however, only iso-salinity surfaces of very low salinity upcone towards the pumping well. The decay process is lengthy; it takes a long time for the upconed saltwater to migrate back to the original horizontal transition zone prior to pumping. However, the wider transition zone caused by hydrodynamic dispersion can never return to the initial one. This indicates that once a pumping well is abandoned because of high salinity, it can be reused for groundwater utilization only after a long time.Quanlin Zhou et al. (To TIPM)

show abstract

Section: Numerical Modelmentioning

confidence: 99%

Saltwater Upconing and Decay Beneath a Well Pumping Above an Interface Zone

2005

View full text Add to dashboard Cite

show abstract

“…E ij has nonzero entries γ|â ij | and γ −1 |â ij | in the ith and jth diagonal positions, respectively, and entry −â ij in the (i, j) and (j, i) positions. The scalar γ may be chosen to keep the same percentage change to the diagonal entriesâ ii andâ jj that are being modified (see [1]). Alternatively, γ may be set to 1 (see [19]) and this is what we employ in our numerical experiments (but see also the weighted strategy in [14] [19].…”

Section: Positive Semidefinite Modification Schemesmentioning

confidence: 99%

On Positive Semidefinite Modification Schemes for Incomplete Cholesky Factorization

Scott¹,

Tůma²

2014

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

Abstract. Incomplete Cholesky factorizations have long been important as preconditioners for use in solving large-scale symmetric positive-definite linear systems. In this paper, we focus on the relationship between two important positive semidefinite modification schemes that were introduced to avoid factorization breakdown, namely, the approach of Jennings and Malik and that of Tismenetsky. We present a novel view of the relationship between the two schemes and implement them in combination with a limited memory approach. We explore their effectiveness using extensive numerical experiments involving a large set of test problems arising from a wide range of practical applications.

show abstract

“…In special cases, there is strong theoretical justification for such modifications [22]. The more general case is developed in [1] where several practical strategies are presented.…”

Section: Diagonal Partial Coloring Problem (Dpcp)mentioning

confidence: 99%

Matrix-free preconditioning using partial matrix estimation

Cullum

Tůma

2006

Bit Numer Math

View full text Add to dashboard Cite

Abstract.We consider matrix-free solver environments where information about the underlying matrix is available only through matrix vector computations which do not have access to a fully assembled matrix. We introduce the notion of partial matrix estimation for constructing good algebraic preconditioners used in Krylov iterative methods in such matrix-free environments, and formulate three new graph coloring problems for partial matrix estimation. Numerical experiments utilizing one of these formulations demonstrate the viability of this approach. (2000): 65F10, 65F50, 49M37, 90C06. AMS subject classification

show abstract

A robust incomplete Choleski‐conjugate gradient algorithm

Cited by 217 publications

References 10 publications

Saltwater Upconing and Decay Beneath a Well Pumping Above an Interface Zone

Saltwater Upconing and Decay Beneath a Well Pumping Above an Interface Zone

On Positive Semidefinite Modification Schemes for Incomplete Cholesky Factorization

Matrix-free preconditioning using partial matrix estimation

Contact Info

Product

Resources

About