Multipreconditioned GMRES for Shifted Systems

An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring the matrix-vector product with the shifted matrix. Furthermore, the multipreconditioned search space is shown to grow only linearly with the number of preconditioners. This allows for a more efficient implementation of the algorithm. The proposed implementation is tested on shifted systems that arise in computational hydrology and the evaluation of different matrix functions. The numerical results indicate the effectiveness of the proposed approach.U.S. National Science Foundation under grant DMS–1418882 and and by the Department of Energy grant DE–SC00165

Estimation of Transmissivities, Heads and Velocities in Steady-State Groundwater Modeling

Modelling groundwater flow can be viewed as two separate problems. The first is identification of the transmissivity of the porous medium. This property fully describes the medium when the type of flow does not vary with time. The second problem is the prediction of the response (output) of the system under different stimuli (inputs), which are given as boundary conditions such as known values of flow, discharge (leakage, pumping, infiltration, etc.), and piezometric head. The research reported here I addresses both of these problems. The theory of random fields provides a powerful method to model the complex variability of transmissivities observed in nature. Choosing this geostatistical approach implies that the other two fields (heads and velocities) must be described as random fields as well. Under this assumption, the natural question to ask is: how can we obtain the best description of the random fields, given all available information? To answer this question, this work presents a new method to estimate the random fields involved in groundwater flow. Its relevant feature is to make maximum use of all available information. The method is based on conditional probability formulas, derived for the case of a Gaussian distribution. A gaussian random field is completely specified by its first two moments: mean and covariance. It is customary to describe the mean as a spatially variable function and the covariance as a function that depends solely on the distance between two points in the field. Both functions depend on parameters that must be estimated from the data. The method of maximum likelihood is used to estimate covariance parameters, while the mean parameters are filtered out by linear transformation of the transmissivity data. A new method was developed to solve the prediction problem. Basically, it estimates the conditional densities of the three random fields using all available data. For this purpose, the flow equation was linearized about a conditional mean of the transmissivity field. Numerical simulations wereI used to test this method; and results are quite satisfactory. A better description of the spatially variable fields was achieved, as manifested by a reduction of the mean squared error of estimation of both the log transmissivity and head fields. The error reduction is directly proportional to the degree of heterogeneity of the log-transmissivity field.Water Resources Research Cente

Application of Hierarchical Matrices to Linear Inverse Problems in Geostatistics

Characterizing the uncertainty in the subsurface is an important step for exploration and extraction of natural resources, the storage of nuclear material and gasses such as natural gas or CO2. Imaging the subsurface can be posed as an inverse problem and can be solved using the geostatistical approach [Kitanidis P.K. (2007) Geophys. Monogr. Ser. 171, 19-30, doi:10.1029/171GM0

Modeling of Reactive Chemical Transport of Leachates from a Utility Fly-Ash Disposal Site

Fly ash from fossil-fuel power plants is commonly slurried and pumped to disposal sites. The utility industry is interested in finding out whether any hazardous constituents might leach from the accumulated fly ash and contaminate ground and surface waters. To evaluate the significance of this problem, a representative site was selected for modeling. FASTCHEM, a computer code developed for the Electric Power Research Institute, was utilized for the simulation of the transport and fate of the fly-ash leachate. The chemical evolution of the leachate was modeled as it migrated along streamtubes defined by the flow model. The modeling predicts that most of the leachate seeps through the dam confining the ash pond. With the exception of ferrous, manganous, sulfate and small amounts of nickel ions, all other dissolved constituents are predicted to discharge at environmentally acceptable concentrations

Borehole water level model for photovoltaic water pumping systems

International audienceHighlights: • A borehole water level model for photovoltaic water pumping systems is developed. • The model is validated against experimental data and has an accuracy of 97%. • The model allows us to study the influence of water resources on the system sizing. • The influence of the static water level on the optimal lifecycle cost is about 11%. • The influence of the drawdown on the optimal lifecycle cost is lower than 2%