The following problem is considered. Given m+1 points {x(i)}(0)(m) in R-n which generate an m-dimensional linear manifold, construct for this manifold a maximally linearly independent basis that consists of vectors of...
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The following problem is considered. Given m+1 points {x(i)}(0)(m) in R-n which generate an m-dimensional linear manifold, construct for this manifold a maximally linearly independent basis that consists of vectors of the form x(i) - x(j). This problem is present in, e.g., stable variants of the secant and interpolation methods, where it is required to approximate the Jacobian matrix f' of a nonlinear mapping f by using values of f computed at m fl points. In this case, it is also desirable to have a combination of finite differences with maximal linear independence. As a natural measure of linear independence, we consider the Hadamard condition number which is minimized to find an optimal combination of m pairs {x(i),x(j)}. We show that the problem is not NP-hard, but can be reduced to the minimum spanning tree problem, which is solved by the greedy algorithm in O(m(2)) time. The complexity of this reduction is equivalent to one m x n matrix-matrix multiplication, and according to the Coppersmith-Winograd estimate, is below O(n(2.376)) for m = n. Applications of the algorithm to interpolation methods are discussed.
The Optimization Test Environment is an interface to efficiently test different optimization solvers. It is designed as a tool for both developers of solver software and practitioners who just look for the best solver...
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The Optimization Test Environment is an interface to efficiently test different optimization solvers. It is designed as a tool for both developers of solver software and practitioners who just look for the best solver for their specific problem class. It enables users to: Choose and compare diverse solver routines;Organize and solve large test problem sets;Select interactively subsets of test problem sets;Perform a statistical analysis of the results, automatically produced as , PDF, and JPG output. The OPTIMIZATION TEST ENVIRONMENT is free to use for research purposes.
Packed beds are widely used to perform solid-catalyzed gas-liquid reactions, e.g., hydrodesulfurization, oxidation, and hydrogenation. The overall performance of packed beds is often governed by local liquid spreading...
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Packed beds are widely used to perform solid-catalyzed gas-liquid reactions, e.g., hydrodesulfurization, oxidation, and hydrogenation. The overall performance of packed beds is often governed by local liquid spreading. In the present work, the dynamics of liquid spreading through a randomly packed three-dimensional bed is investigated using particle-resolved volume-of-fluid simulations. The effect of particle surface-wettability ( theta) at varying particle diameter ( d(p)) on the relative contributions of forces governing the dynamics of liquid spreading is analyzed using the Ohnesorge (Oh(I)), Weber ( We(I)), and AB(I) (proposed in the present work) numbers. With the help of simulated liquid spreading and these numbers, we show that the contribution of inertial force is significant at the beginning of liquid spreading irrespective of theta as well as d(p) and promotes lateral liquid spreading (AB(I) > 1, We(I) > 1). Once the dominance of inertial force diminishes, the capillary force leads to a substantial increase in the lateral spreading (AB(I) > 1, We(I) < 1). In the final stages, the gravitational force dominates restricting the lateral liquid spreading (AB(I) < 1). Furthermore, we have proposed a regime map constructed using AB(I) and We(I), which provides a relationship between different forces and the resultant liquid spreading at breakthrough. We also show that the dominance of capillary force (AB(I) > 1, We(I )< 1) results in the highest lateral spreading, whereas the flow dominated by inertial (AB(I) > 1, We(I) > 1) and gravitational force ( AB(I) (sic) 1) leads to intermediate and least lateral liquid spreading, respectively.
In this paper a parallel algorithm for simulated annealing (SA) in the continuous case, the Multiple Trials and Adaptive Supplementary Search, MTASS algorithm, is presented. it is based on a combination of multiple tr...
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In this paper a parallel algorithm for simulated annealing (SA) in the continuous case, the Multiple Trials and Adaptive Supplementary Search, MTASS algorithm, is presented. it is based on a combination of multiple trials, local improved searches and an adaptive cooling schedule. The results in optimizing some standard test problems are compared with some SA sequential algorithms and another parallel probabilistic algorithm.
Packed bed reactors are widely used to perform solid-catalyzed gas-phase reactions and local turbulence is known to influence heat and mass transfer characteristics. We have investigated turbulence characteristics in ...
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Packed bed reactors are widely used to perform solid-catalyzed gas-phase reactions and local turbulence is known to influence heat and mass transfer characteristics. We have investigated turbulence characteristics in a packed bed of 113 spherical particles by performing particle-resolved Reynolds-averaged Navier-Stokes (RANS) simulations, Large Eddy Simulation (LES), and Direct Numerical Simulation (DNS). The predictions of the RANS and LES simulations are validated with the lattice Boltzmann method (LBM)-based DNS at particle Reynolds number (Re-p) of 600. The RANS and LES simulations can predict the velocity, strain rate, and vorticity with a reasonable accuracy. Due to the dominance of enhanced wall-function treatment, the turbulence characteristics predicted by the epsilon-based models are found to be in a good agreement with the DNS. The omega-based models under-predicted the turbulence quantities by several orders of magnitude due to their inadequacy in handling strongly wall-dominated flows at low Re-p. Using the DNS performed at different Re-p, we also show that the onset of turbulence occurs between 200 <= Rep <= 250.
作者:
Burdakov, OPCERFACS
Parallel Algorithms Team 31057 Toulouse Cedex 42 Avenue Gustave Coriolis France
The following problem is considered. Given m + 1 points {x(i)}(m)(0) in IR(n) which generate an m-dimensional linear manifold, construct for this manifold a maximally linearly independent basis that consists of vector...
The following problem is considered. Given m + 1 points {x(i)}(m)(0) in IR(n) which generate an m-dimensional linear manifold, construct for this manifold a maximally linearly independent basis that consists of vectors of the form x(i) - x(j). This problem is present in, e.g., stable variants of the secant method, where it is required to approximate the Jacobian matrix f' of a nonlinear mapping f by using valves of f computed at m + 1 points. In this case, it is also desirable to have a combination of finite differences with maximal linear independence. As a natural measure of linear independence, we consider a functional which is maximized to find an optimal combination of m pairs {x(i), x(j)}. We show that the problem is not of combinatorial complexity but can be reduced to the minimum spanning tree (MST) problem, which is solved by an MST-type algorithm in O(m(2)n) time.
作者:
Hamma, B.Parallel Algorithms Team
CERFACS European Centre for Research Advanced Training in Scientific Computing 42 av. Coriolis Toulouse-Cedex F-31057 France
This paper describes the software developed at CNES within the context of the VESTA Franco-Soviet program, for the optimization of interplanetary trajectories. The sequentiel software, intended for the determination o...
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作者:
Fuchs, MartinCERFACS
Parallel Algorithms Team 42 Avenue Gaspard Coriolis Toulouse 31057 France
Past studies of uncertainty handling with polyhedral clouds have already shown strength in dealing with higher dimensional uncertainties in robust optimisation, even in case of partial ignorance of statistical informa...
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The gyrokinetic Poisson equation arises as a subproblem of Tokamak fusion reactor simulations. It is often posed on disk-like cross sections of the Tokamak that are represented in generalized polar coordinates. On the...
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The gyrokinetic Poisson equation arises as a subproblem of Tokamak fusion reactor simulations. It is often posed on disk-like cross sections of the Tokamak that are represented in generalized polar coordinates. On the resulting curvilinear anisotropic meshes, we discretize the differential equation by finite differences or low order finite elements. Using an implicit extrapolation technique similar to multigrid tau-extrapolation, the approximation order can be increased. This technique can be naturally integrated in a matrix-free geometric multigrid algorithm. Special smoothers are developed to deal with the mesh anisotropy arising from the curvilinear coordinate system and mesh grading.
In this work we present a predictive analytical model that encompasses the performance and scaling characteristics of an important ASCI application. SAGE (SAIC's Adaptive Grid Eulerian hydrocode) is a multidimensi...
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