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A greedy algorithm for the optimal basis problem

BIT NUMERICAL MATHEMATICS 1997年第3期37卷 591-599页

作者： Burdakov, O CERFACS PARALLEL ALGORITHMS TEAM F-31057 TOULOUSE FRANCE

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.

关键词： optimal basis problem the Hadamard condition number minimum spanning tree problem greedy algorithm secant approximation of derivatives interpolation methods

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The optimization test environment

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OPTIMIZATION AND ENGINEERING 2014年第2期15卷 443-468页

作者： Domes, Ferenc Fuchs, Martin Schichl, Hermann Neumaier, Arnold Univ Vienna Fac Math A-1090 Vienna Austria CERFACS Parallel Algorithms Team F-31057 Toulouse France

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.

关键词： Test environment Optimization Solver benchmarking Solver comparison

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Particle-resolved simulations of local liquid spreading in packed beds: Effect of wettability at varying particle size

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PHYSICS OF FLUIDS 2022年第6期34卷 1-14页

作者： Ambekar, Aniket S. Ruede, Ulrich Buwa, Vivek V. Indian Inst Technol Delhi Dept Chem Engn Delhi India Univ Erlangen Nurnberg Chair Syst Simulat Nurnberg Germany CERFACS Parallel Algorithms Team Toulouse France

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.

关键词： Packed beds

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parallel continuous simulated annealing for global optimization

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OPTIMIZATION METHODS & SOFTWARE 2000年第2期13卷 95-116页

作者： Hamma, B Viitanen, S Törn, A ILOG SA Resource Optimizat Consulting F-92253 Gentilly France CERFACS Parallel Algorithms Team F-31057 Toulouse France Abo Akad Univ Dept Comp Sci FIN-20520 Turku Finland

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.

关键词： simulated annealing global optimization parallel algorithms

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Particle-resolved turbulent flow in a packed bed: RANS, LES, and DNS simulations

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AICHE JOURNAL 2023年第1期69卷 e17615-e17615页

作者： Ambekar, Aniket S. Schwarzmeier, Christoph Ruede, Ulrich Buwa, Vivek V. Indian Inst Technol Delhi Dept Chem Engn New Delhi 110016 India Univ Erlangen Nurnberg Dept Comp Sci Chair Syst Simulat Erlangen Germany CERFACS Parallel Algorithms Team Toulouse France

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.

关键词： Direct Numerical Simulations Large Eddy Simulations Packed bed Particle-resolved simulations Turbulence models

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On using the minimum spanning tree algorithm for optimal secant approximation of derivatives

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ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK 1996年第SUPPL. 3期76卷 389-390页

作者： Burdakov, OP CERFACS 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 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.

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parallel optimization of interplanetary trajectories 3rd

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Proceedings of the 1996 3rd International Workshop on Applied parallel Computing, PARA

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

ISBN: (纸本)3540620958

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 of multiple flyby trajectories and their optimization, was developed previously in collaboration with CNES and LAO of Paul Sabatier University, Toulouse, France. In this software, an impulse manoeuvre is performed at each flyby. The possibility to add an intermediate manoeuvre between flybys and the use of the swing-by aim to reduce the total trajectory costs. The optimization routines are parallelized. © Springer-Verlag Berlin Heidelberg 1996.

关键词： Interplanetary trajectories Lambert problem Multiple-flyby parallel optimization Swing-by

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Simulated polyhedral clouds in robust optimisation

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International Journal of Reliability and Safety 2012年第1-3期6卷 65-81页

作者： Fuchs, Martin CERFACS 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 information. However, the number of function evaluations necessary to quantify and propagate the uncertainties has been too high to be useful in many real-life applications with respect to limitations of computational cost. In this paper, we propose a simulation-based approach for optimisation over a polyhedron, inspired by the Cauchy deviates method. Thus, we achieve a computationally efficient method to compute worst-case scenarios with polyhedral clouds which we embed in a robust optimisation problem formulation. We apply the method to two test cases from space system design. © 2012 Inderscience Enterprises Ltd.

关键词： Optimization

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Implicitly Extrapolated Geometric Multigrid on Disk-Like Domains for the Gyrokinetic Poisson Equation from Fusion Plasma Applications

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JOURNAL OF SCIENTIFIC COMPUTING 2022年第1期91卷 1-27页

作者： Kuehn, Martin J. Kruse, Carola Ruede, Ulrich German Aerosp Ctr DLR Inst Software Technol Dept High Performance Comp Cologne Germany CERFACS Ctr Europeen Rech & Format Avancee Calcul Parallel Algorithms Team 42 Ave Gaspard Coriolis F-31057 Toulouse 01 France Friedrich Alexander Univ Erlangen Nurnberg Cauerstr 11 D-91058 Erlangen Germany

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.

关键词： Fusion plasma Disk-like Cross section Multigrid Extrapolation

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Predictive performance and scalability modeling of a large-scale application 01

Predictive performance and scalability modeling of a large-s...

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2001 ACM/IEEE Conference on Supercomputing, SC 2001

作者： Kerbyson, D.J. Alme, H.J. Hoisie, A. Petrini, F. Wasserman, H.J. Gittings, M. Los Alamos National Laboratory Parallel Architectures and Performance Team CCS-3 Modeling Algorithms and Informatics Group Los AlamosNM87545 United States Saic Los Alamos National Laboratory United States

ISBN: (纸本)158113293X

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 multidimensional hydrodynamics code with adaptive mesh refinement. The model is validated against measurements on several systems including ASCI Blue Mountain, ASCI White, and a Compaq Alphaserver ES45 system showing high accuracy. It is parametric - - basic machine performance numbers (latency, MFLOPS rate, bandwidth) and application characteristics (problem size, decomposition method, etc.) serve as input. The model is applied to add insight into the performance of current systems, to reveal bottlenecks, and to illustrate where tuning efforts can be effective. We also use the model to predict performance on future systems. © 2001 ACM.

关键词： parallel architectures

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