Comparison of some parallel Krylov solvers for large scale groundwater contaminant transport simulations

Some popular iterative solvers for non-symmetric systems arising from the finite-element discretization of three-dimensional groundwater contaminant transport problem are implemented and compared on distributed memory parallel platforms. This paper attempts to determine which solvers are most suitable for the contaminant transport problem under varied conditions for large scale simulations on distributed parallel platforms. The original parallel implementation was targeted for the 1024 node Intel paragon platform using explicit message passing with the NX library. This code was then ported to SGI Power Challenge Array, Convex Exemplar, and Origin 2000 machines using an MPI implementation. The performance of these solvers is studied for increasing problem size, roughness of the coefficients, and selected problem scenarios. These conditions affect the properties of the matrix and hence the difficulty level of the solution process. Performance is analyzed in terms of convergence behavior, overall time, parallel efficiency, and scalability. The solvers that are presented are BiCGSTAB, GMRES, ORTHOMIN, and CGS. A simple diagonal preconditioner is used in this parallel implementation for all the methods. The results indicate that all methods are comparable in performance with BiCGSTAB slightly outperforming the other methods for most problems. The authors achieved very good scalability in all the methods up to 1024 processors of the Intel Paragon XPS/150. They demonstrate scalability by solving 100 time steps of a 40 million element problem in about 5 minutes using either BiCGSTAB or GMRES

The Battle of the Water Networks II (BWN-II)

The Battle of the Water Networks II (BWN-II) is the latest of a series of competitions related to the design and operation of water distribution systems (WDSs) undertaken within the Water Distribution Systems Analysis (WDSA) Symposium series. The BWN-II problem specification involved a broadly defined design and operation problem for an existing network that has to be upgraded for increased future demands, and the addition of a new development area. The design decisions involved addition of new and parallel pipes, storage, operational controls for pumps and valves, and sizing of backup power supply. Design criteria involved hydraulic, water quality, reliability, and environmental performance measures. Fourteen teams participated in the Battle and presented their results at the 14th Water Distribution Systems Analysis (WDSA 2012) conference in Adelaide, Australia, September 2012. This paper summarizes the approaches used by the participants and the results they obtained. Given the complexity of the BWN-II problem and the innovative methods required to deal with the multi-objective, high dimensional and computationally demanding nature of the problem, this paper represents a snap-shot of state of the art methods for the design and operation of water distribution systems. A general finding of this paper is that there is benefit in using a combination of heuristic engineering experience and sophisticated optimization algorithms when tackling complex real-world water distribution system design problems.Angela Marchi...Angus R. Simpson, Aaron C. Zecchin, Holger R. Maier...Christopher Stokes, Wenyan Wu, Graeme C. Dandy...et al

The Battle of the Water Networks II (BWN-II)

The Battle of the Water Networks II (BWN-II) is the latest of a series of competitions related to the design and operation of water distribution systems (WDSs) undertaken within the Water Distribution Systems Analysis (WDSA) Symposium series. The BWN-II problem specification involved a broadly defined design and operation problem for an existing network that has to be upgraded for increased future demands, and the addition of a new development area. The design decisions involved addition of new and parallel pipes, storage, operational controls for pumps and valves, and sizing of backup power supply. Design criteria involved hydraulic, water quality, reliability, and environmental performance measures. Fourteen teams participated in the Battle and presented their results at the 14th Water Distribution Systems Analysis (WDSA 2012) conference in Adelaide, Australia, September 2012. This paper summarizes the approaches used by the participants and the results they obtained. Given the complexity of the BWN-II problem and the innovative methods required to deal with the multi-objective, high dimensional and computationally demanding nature of the problem, this paper represents a snap-shot of state of the art methods for the design and operation of water distribution systems. A general finding of this paper is that there is benefit in using a combination of heuristic engineering experience and sophisticated optimization algorithms when tackling complex real-world water distribution system design problems.Angela Marchi...Angus R. Simpson, Aaron C. Zecchin, Holger R. Maier...Christopher Stokes, Wenyan Wu, Graeme C. Dandy...et al

Impact of nonideal transport upon the effectiveness of pump-and-treat groundwater remediation: A computational investigation

The impact of various nonidealities affecting pump and treat remediation was analyzed using numerical simulations. In particular, the effect of the following important non-idealities was investigated: spatial variability of hydraulic conductivity (K-field heterogeneity), spatial variability of sorption parameters, rate-limited desorption, and the combined effects of the latter two with K-field heterogeneity. Heterogeneous K-fields are modelled as spatially correlated lognormal random fields in this thesis. A hypothetical problem scenario was used to illustrate the effects of most of these nonidealities. The effect of K-field heterogeneity was also examined for a plume formed by naturally leaching conditions.Monte Carlo simulations were used to analyze the impact of uncertainty of K-field heterogeneity on the uncertainty of cleanup times. For the highest K-field variability of \sigma\sb{\rm Y} = 2.0, the uncertainty in the 95% cleanup time estimated by coefficient of variation was approximately 0.2. Some analytical results derived for travel time moments, radial velocity variances, and effective hydraulic conductivity were compared with the numerical results.Efficient codes were developed to for the solution of three-dimensional groundwater flow and solute transport problems on supercomputers. The codes were developed for Cray Y-MP/C90 which is a shared memory vector/parallel computer and the connection machine CM-5 which is a distributed memory massively parallel computer. For the groundwater flow problem, a finite-element/finite-difference code coupled with a conjugate gradient matrix solver was developed to work efficiently on both machines. For the solute transport problem, a finite-element/finite-difference code coupled with a GMRES matrix solver and a particle tracking code were developed for both machines.U of I OnlyETDs are only available to UIUC Users without author permissio

Multigrid and Krylov Solvers for Large Scale Finite Element Groundwater Flow Simulations on Distributed Memory Parallel Platforms

In this report we present parallel solvers for large linear systems arising from the finite-element discretization of the three-dimensional steady-state groundwater flow problem. Our solvers are based on multigrid and Krylov subspace methods. The parallel implementation is based on a domain decomposition strategy with explicit message passing using NX and MPI libraries. We have tested our parallel implementations on the Intel Paragon XP/S 150 supercomputer using up to 1024 parallel processors and on other parallel platforms such as SGI/Power Challenge Array, Cray/SGI Origin 2000, Convex Exemplar SPP-1200, and IBM SP using up to 64 processors. We show that multigrid can be a scalable algorithm on distributed memory machines. We demonstrate the effectiveness of parallel multigrid based solvers by solving problems requiring more than 70 million nodes in less than a minute. This is more than 25 times faster than the diagonal preconditioned conjugate gradient method which is one of the more popular methods for large sparse linear systems. Our results also show that multigrid as a stand alone solver works best for problems with smooth coefficients, but for rough coefficients it is best used as a preconditioner for a Krylov subspace method such as the conjugate gradient method. We show that even for extremely heterogeneous systems the multigrid pre-conditioned conjugate gradient method is at least 10 times faster than the diagonally preconditioned conjugate gradient method

Efficient Parallel Multigrid based Solvers for Large Scale Groundwater Flow Simulations

In this paper we present parallel solvers for large linear systems arising from the finite-element discretization of three-dimensional groundwater flow problems. We have tested our parallel implementations on the Intel Paragon XP/S 150 supercomputer using up to 1024 parallel processors. Our solvers are based on multigrid and Krylov subspace methods. Our goal is to combine powerful algorithms and current generation high performance computers to enhance the capabilities of computer models for groundwater modeling. We show that multigrid can be a scalable algorithm on distributed memory machines. We demonstrate the effectiveness of parallel multigrid based solvers by solving problems requiring more than 64 million nodes in less than a minute. Our results show that multigrid as a stand alone solver works best for problems with smooth coefficients, but for rough coefficients it is best used as a preconditioner for a Krylov subspace method. Keywords Hydrology, Multiprocessors, Numerical meth..