A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems

Commun. Numer. Meth. Engng.

2002

Preconditioning techniques based on ILU decomposition, on Frobenius norm minimization and on factorized sparse approximate inverse are considered. These algorithms are applied with conjugate gradient-type methods, namely Bi-CGSTAB, QMR and TFQMR for the solution of complex, large, sparse linear systems. The results of numerical experiments in scalar environment with matrices arising from transport in porous media, quantum chemistry, structural dynamics and electromagnetism are analysed. The preconditioner that appears most significant in parallel environment (based on factorized sparse approximate inverse) is then employed on a Cray T3E supercomputer. The experimental results show the satisfactory parallel performance of the proposed algorithm

Section: Quantum Chemistrymentioning

confidence: 99%

“…In the experiments, we set = 10 −15 [3,24]. Observe that to the preconditioned residual norm verifying the stopping criterion of order of 10…”

Section: Notes On Preconditioning Implementationmentioning

confidence: 99%

Numerical performance of preconditioning techniques for the solution of complex sparse linear systems

Mazzia

Commun. Numer. Meth. Engng.

2002

“…The finite element discretization of both the sandy and the clayey units produces large, sparse linear systems. Appropriate numerical techniques to efficiently solve these systems have been devised [2,8,9,16,21]. Numerical procedures based on iterative methods were shown to be highly effective.…”

Section: G Pin1 a N D F Sartorettomentioning

confidence: 99%

“…Numerical procedures based on iterative methods were shown to be highly effective. Block SOR or GaussSeidel methods naturally arise in this context [9]. However, the degree of parallelization attainable using those schemes was shown to be lower than that obtained by a Block Jacobi iterative strategy [19].…”

Section: G Pin1 a N D F Sartorettomentioning

confidence: 99%

“…the permeability and the elastic storage of the aquitards, depend on, the hydraulic head, thus the flow is governed by tronlinear partial differential equations. An efficient strategy to easily resolve the nonlinearity was developed [9]. A finite difference, time stepping scheme is used for the time integration of the flow equations.…”

Section: G Pin1 a N D F Sartorettomentioning

confidence: 99%

See 1 more Smart Citation

A Parallel Finite Element Code for Nonlinear Leaky Aquifer Systems

Parallel Algorithms and Applications

Sartoretto

1999

Porollel Algarirhmc and Appliculiow. VoI. 13. pp. 345,161 0 1999 OPA (Ovc-r Publirhcrs Arsoeiution) N.V. Rcprina available directly from the publirhcr Published by licenw undcr Photocopying pcmittcd by license only thc Gordon and Breach Science Publirhcn imprint.Developing parallel codes for computing the nonlinear flow in multiaquifer porous systems is an important task both for improving model efficiency and for performing large real-life simulations. Multiaquifer systems consist of sandy and clayey alternating layers. In this paper, highly compressible multiaquifer systems are considered, where some hydraulic parameters depend on the potential head, thus the flow inside some layers is governed by nonlinear equations. An erective procedure for solving these equations is developed, relying upon the partition of the solution procedure into layer-wise steps. By assigning to each processor the computation of the flow inside a suitable set of layers, the iterative solution procedure can be efficiently implemented on a parallel super-computer. Using such a domain decomposition strategy, a satisfactory degree of parallelization is achieved when computing the flow in a realistic nonlinear multiaquifer system, employing a CRAY T3D massively parallel computer. Performing test simulations on real-life multiaquifer systems, the recorded speed-ups are as large as 1.89, 3.34. 5.37, with 2, 4, 8 processors, respectively. The importance of load balance and information exchange in casting the parallel performances of the code is also analyzed.

Parallel block iterative method for multiaquifer flow models

Numer. Methods Partial Differential Eq.

Teatini

1997

Self Cite

Flow in a multiaquifer porous system can be simulated by the so-called "quasi three-dimensional" models. When heterogeneous and/or aquitards with nonlinear hydrogeologic behavior are considered, a fully numerical approach is required for the model solution. If the finite element method is used to integrate the partial differential flow equations, the final solution of large systems is required. In the present article, an original iterative solution strategy is developed. The global system is decoupled into a number of smaller subsystems consistent with the geologic structure (aquitards and aquifers) of the multiaquifer system. The aquifer and the aquitard equations are solved separately with the modified conjugate gradient and the Thomas algorithms, respectively, while the final coupled solution is obtained with an iterative procedure equivalent to a Block Jacobi scheme. The procedure can be efficiently implemented on a parallel super-computer distributing the computational load, so that two successive blocks (related to an aquifer and the underlying aquitard) are solved on the same processor. The procedure is analyzed with linear porous media, where the convergence is theoretically ensured. The results obtained with a realistic linear multiaquifer system, employing a massively parallel computer like the CRAY T3D, have pointed out the high degree of parallelization of the algorithm. Comparison with the parallel implementation of the Block SOR and Block Gauss-Seidel schemes shows that parallel Block Jacobi performs significantly better with a reduction of the elapsed times, which depends on the rate of leakage between neighboring aquifers.