作者：
GOLUB, GHNASH, SGProfessor
Computer Science Department Stanford University Stanford CA 94305. Graduate student
Computer Science Department Stanford University Stanford CA 94305
A method is developed that computes an exact nonorthogonal analysis of variance using cell means. The method is iterative and does not require that the nonorthogonal design matrix be stored or formed. At each stage in...
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A method is developed that computes an exact nonorthogonal analysis of variance using cell means. The method is iterative and does not require that the nonorthogonal design matrix be stored or formed. At each stage in the process, a balanced analysis of variance problem must be solved. A monotonicity property for the estimates of the regression sum of squares is derived that could be used to minimize iteration in hypothesis testing. An application of the algorithm to the solution of analysis of covariance problems is also given.
We have performed an ab initio study of the volume dependence of elastic and lattice dynamical properties of chalcopyrite semiconductor CuAlSe2. The calculations have been carried out within the local density function...
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We have performed an ab initio study of the volume dependence of elastic and lattice dynamical properties of chalcopyrite semiconductor CuAlSe2. The calculations have been carried out within the local density functional approximation using norm-conserving pseudopotentials and a plane-wave basis. Born effective charge tensors, dielectric permittivity tensors. the phonon frequencies at the Brillouin zone centre and their Gruneisen parameters are calculated using density functional perturbation theory. We compare the Gruneisen parameters of the calculated quantities with those of zinc-blende type materials and find similar trends. Calculated elastic stiffness constants show pseudocubic behaviour.
The specification of a correct background-error covariance matrix is a key issue in data assimilation schemes. The Ensemble Kalman Filter (EnKF) aims at providing simulations of analysis and background errors and then...
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The specification of a correct background-error covariance matrix is a key issue in data assimilation schemes. The Ensemble Kalman Filter (EnKF) aims at providing simulations of analysis and background errors and then gives a way to determine this background-error covariance matrix. The EnKF can be transposed to variational ensemble assimilation, where a set of perturbed variational analyses are performed. In this case, however, there is an evident important additional cost associated with the use of multiple minimizations. The aim of the paper is to investigate different techniques to reduce the cost of the multiple minimizations that have to be performed. In particular, the use is investigated of a preconditioning technique based on Ritz eigenpairs resulting from a first minimization performed by a combined Lanczos/conjugate-gradient algorithm. The possibility is also studied of improving the starting point of a new perturbed solution, with Lanczos vectors issued from a single prior unperturbed or perturbed minimization. This appears to provide a first significant reduction in the cost of the new minimization. Finally, a new approach is proposed to generalize the previous idea to the use of multiple sets of Lanczos vectors issued from an ensemble of perturbed assimilations. The application of this procedure to a simplified analysis problem shows encouraging results, as it appears to be a possible way for reducing the global cost of an ensemble variational assimilation. Moreover, this seems to provide an efficient strategy for parallelizing such an ensemble variational assimilation but also the deterministic variational assimilation itself. Copyright (c) 2012 Royal Meteorological Society
Using quantum-mechanical simulations based on density-functional perturbation theory, we address the problem of stability of MgSiO3 perovskite to decomposition into MgO and SiO2 at pressures and temperatures of the Ea...
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Using quantum-mechanical simulations based on density-functional perturbation theory, we address the problem of stability of MgSiO3 perovskite to decomposition into MgO and SiO2 at pressures and temperatures of the Earth's lower mantle. We show that MgSiO3 perovskite (and its post-perovskite phase) is more stable than the mixture of oxides throughout the pressure-temperature regime of the Earth's mantle. Structural stability and lattice dynamics of phases in the system MgO-SiO2 are discussed.
The major emphasis of this work is the development of a stabilized finite element method for solving incompressible Navier-Stokes equations with stochastic input data. The polynomial chaos expansion is used to represe...
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The major emphasis of this work is the development of a stabilized finite element method for solving incompressible Navier-Stokes equations with stochastic input data. The polynomial chaos expansion is used to represent stochastic processes in the variational problem, resulting in a set of deterministic variational problems to be solved for each Wiener polynomial chaos. To obtain the chaos coefficients in the corresponding deterministic incompressible Navier-Stokes equations, we combine the modified method of characteristics with the finite element discretization. The obtained Stokes problem is solved using a robust conjugate-gradient algorithm. This algorithm avoids projection procedures and any special correction for the pressure. These numerical techniques associate the geometrical flexibility of the finite element method with the ability offered by the modified method of characteristics to solve convection-dominated problems using time steps larger than its Eulerian counterpart. Numerical results are shown for the benchmark problems of driven cavity flow and backward-facing step flow. We also present numerical results for a problem of stochastic natural convection. It is found that the proposed stabilized finite element method offers a robust and accurate approach for solving the stochastic incompressible Navier-Stokes equations, even when high Reynolds and Rayleigh numbers are used in the simulations.
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