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1.
    
We present the open source Lattice Boltzmann solver Musubi. It is part of the parallel simulation framework APES, which utilizes octrees to represent sparse meshes and provides tools from automatic mesh generation to post-processing. The octree mesh representation enables the handling of arbitrarily complex simulation domains, even on massively parallel systems. Local grid refinement is implemented by several interpolation schemes in Musubi. Various kernels provide different physical models based on stream-collide algorithms. These models can be computed concurrently and can be coupled with each other. This paper explains our approach to provide a flexible yet scalable simulation environment and elaborates its design principles and implementation details. The efficiency of our approach is demonstrated with a performance evaluation on two supercomputers and a comparison to the widely used Lattice Boltzmann solver Palabos.  相似文献   

2.
This article describes the computation of pipe flow in the entrance region. The pressure distribution and flow characteristics, particularly the effect of vorticity in the vicinity of the wall, were analyzed for moderate Reynolds numbers (Re) ranging from 500 to 10,000. It was found, for the first time, that a large pressure gradient in the radial direction exists near the pipe inlet. The pressure gradient is caused by the radial component of the curl of vorticity, which decreases as Re increases. The pressure at the wall is lower than that at the central core for Re ≤ 5000. This result is beyond the scope of the boundary-layer assumption for pressure, although it applies to flows at high Reynolds numbers.  相似文献   

3.
Optimization algorithms coupled with computational fluid dynamics are used for wind turbines airfoils design. This differs from the traditional aerospace design process since the lift-to-drag ratio is the most important parameter and the angle of attack is large. Computational fluid dynamics simulations are performed with the incompressible Reynolds-averaged Navier–Stokes equations in steady state using a one equation turbulence model. A detailed validation of the simulations is presented and a computational domain larger than suggested in literature is shown to be necessary. Different approaches to parallelization of the computational code are addressed. Single and multiobjective genetic algorithms are employed and artificial neural networks are used as a surrogate model. The use of artificial neural networks is shown to reduce computational time by almost 50%.  相似文献   

4.
Parallel processors are becoming an attractive option for meeting the requirements to solve large nonlinear optimization problems and the partially separable methods are ideal candidates for parallel computing. This paper proposes implementation techniques for such methods. Computational experiments on an IBM 3090-200 and on a simulated multiprocessor are presented. The performance of both implementations is compared against a reference serial implementation.  相似文献   

5.
Two families of derivative free two-point iterative methods for solving nonlinear equations are constructed. These methods use a suitable parametric function and an arbitrary real parameter. It is proved that the first family has the convergence order four requiring only three function evaluations per iteration. In this way it is demonstrated that the proposed family without memory supports the Kung-Traub hypothesis (1974) on the upper bound 2n of the order of multipoint methods based on n + 1 function evaluations. Further acceleration of the convergence rate is attained by varying a free parameter from step to step using information available from the previous step. This approach leads to a family of two-step self-accelerating methods with memory whose order of convergence is at least and even in special cases. The increase of convergence order is attained without any additional calculations so that the family of methods with memory possesses a very high computational efficiency. Numerical examples are included to demonstrate exceptional convergence speed of the proposed methods using only few function evaluations.  相似文献   

6.
Acceleration devices are very important to speed up interval global optimization algorithms. We propose here two techniques which can be applied in addition to other known techniques. Firstly, we propose a test based on the one-dimensional Newton iteration to discard or split the current box. This test is usually cheap and it is likely to be successful when a good approximation of the minimum is known early. The other technique proposed deals with parallelization. We propose to share the task of the manager process among other non-idle processes in such a way that not only one process is responsible for the load balancing. Experimental results presented show that both techniques yield significant improvements in many cases.  相似文献   

7.
Truncated-Newton methods are a class of optimization methods suitable for large scale problems. At each iteration, a search direction is obtained by approximately solving the Newton equations using an iterative method. In this way, matrix costs and second-derivative calculations are avoided, hence removing the major drawbacks of Newton's method. In this form, the algorithms are well-suited for vectorization. Further improvements in performance are sought by using block iterative methods for computing the search direction. In particular, conjugate-gradient-type methods are considered. Computational experience on a hypercube computer is reported, indicating that on some problems the improvements in performance can be better than that attributable to parallelism alone.Partially supported by Air Force Office of Scientific Research grant AFOSR-85-0222.Partially supported by National Science Foundation grant ECS-8709795, co-funded by the U.S. Air Force Office of Scientific Research.  相似文献   

8.
Several techniques for global optimization treat the objective functionf as a force-field potential. In the simplest case, trajectories of the differential equationmx=–f sample regions of low potential while retaining the energy to surmount passes which might block the way to regions of even lower local minima. Apotential transformation is an increasing functionV:. It determines a new potentialg=V(f), with the same minimizers asf and new trajectories satisfying . We discuss a class of potential transformations that greatly increase the attractiveness of low local minima.These methods can be applied to constrained problems through the use of Lagrange multipliers. We discuss several methods for efficiently computing approximate Lagrange multipliers, making this approach practical.  相似文献   

9.
Interval analysis is a powerful tool which allows to design branch-and-bound algorithms able to solve many global optimization problems. In this paper we present new adaptive multisection rules which enable the algorithm to choose the proper multisection type depending on simple heuristic decision rules. Moreover, for the selection of the next box to be subdivided, we investigate new criteria. Both the adaptive multisection and the subinterval selection rules seem to be specially suitable for being used in inequality constrained global optimization problems. The usefulness of these new techniques is shown by computational studies.  相似文献   

10.
Stochastic programming is recognized as a powerful tool to help decision making under uncertainty in financial planning. The deterministic equivalent formulations of these stochastic programs have huge dimensions even for moderate numbers of assets, time stages and scenarios per time stage. So far models treated by mathematical programming approaches have been limited to simple linear or quadratic models due to the inability of currently available solvers to solve NLP problems of typical sizes. However stochastic programming problems are highly structured. The key to the efficient solution of such problems is therefore the ability to exploit their structure. Interior point methods are well-suited to the solution of very large non-linear optimization problems. In this paper we exploit this feature and show how portfolio optimization problems with sizes measured in millions of constraints and decision variables, featuring constraints on semi-variance, skewness or non-linear utility functions in the objective, can be solved with the state-of-the-art solver.  相似文献   

11.
We present a new parallel method for verified global optimization, using a centralized mediator for the dynamic load balancing. The new approach combines the advantages of two previous models, the master slave model and the processor farm. Numerical results show the efficiency of this new method. For a large number of problems at least linear speedup is reached. The efficiency of this new method is also confirmed by a comparison with other parallel methods for verified global optimization. A theoretical study proves that using the best-first strategy to choose the next box for subdivision, no real superlinear speedup may be expected concerning the number of iterations. Moreover, the potential of parallelization of methods of verified global optimization is discussed in general.  相似文献   

12.
覃正  陈绍汀 《应用数学》1996,9(3):369-372
本文面向SIMD(SingleInstructionStream,MultipleDataStream)型机设计同步并行算法,对刚性动力学方程新算法提出了二层并行计算路径.同时,还讨论了并行计算的有关算法特性.算法分析表明,本文的算法是可行和高效的.  相似文献   

13.
We introduce a master–worker framework for parallel global optimization of computationally expensive functions using response surface models. In particular, we parallelize two radial basis function (RBF) methods for global optimization, namely, the RBF method by Gutmann [Gutmann, H.M., 2001a. A radial basis function method for global optimization. Journal of Global Optimization 19(3), 201–227] (Gutmann-RBF) and the RBF method by Regis and Shoemaker [Regis, R.G., Shoemaker, C.A., 2005. Constrained global optimization of expensive black box functions using radial basis functions, Journal of Global Optimization 31, 153–171] (CORS-RBF). We modify these algorithms so that they can generate multiple points for simultaneous evaluation in parallel. We compare the performance of the two parallel RBF methods with a parallel multistart derivative-based algorithm, a parallel multistart derivative-free trust-region algorithm, and a parallel evolutionary algorithm on eleven test problems and on a 6-dimensional groundwater bioremediation application. The results indicate that the two parallel RBF algorithms are generally better than the other three alternatives on most of the test problems. Moreover, the two parallel RBF algorithms have comparable performances on the test problems considered. Finally, we report good speedups for both parallel RBF algorithms when using a small number of processors.  相似文献   

14.
This paper introduces a new derivative-free class of mesh adaptive direct search (MADS) algorithms for solving constrained mixed variable optimization problems, in which the variables may be continuous or categorical. This new class of algorithms, called mixed variable MADS (MV-MADS), generalizes both mixed variable pattern search (MVPS) algorithms for linearly constrained mixed variable problems and MADS algorithms for general constrained problems with only continuous variables. The convergence analysis, which makes use of the Clarke nonsmooth calculus, similarly generalizes the existing theory for both MVPS and MADS algorithms, and reasonable conditions are established for ensuring convergence of a subsequence of iterates to a suitably defined stationary point in the nonsmooth and mixed variable sense.  相似文献   

15.
We introduce and discuss a combination of methods and options that aim at the aerodynamical optimization of a flow around an arbitrary aircraft shape. The flow is governed by the Euler equations, discretized by a mixed element-volume method on a fixed unstructured tetrahedrization. The shape parametrization relies on the skin of the above mesh through a hierarchical representation. Descent-type and one-shot algorithms are devised and adapted to the solution of a few model problems.  相似文献   

16.
Multi-step quasi-Newton methods for optimization   总被引:4,自引:0,他引:4  
Quasi-Newton methods update, at each iteration, the existing Hessian approximation (or its inverse) by means of data deriving from the step just completed. We show how “multi-step” methods (employing, in addition, data from previous iterations) may be constructed by means of interpolating polynomials, leading to a generalization of the “secant” (or “quasi-Newton”) equation. The issue of positive-definiteness in the Hessian approximation is addressed and shown to depend on a generalized version of the condition which is required to hold in the original “single-step” methods. The results of extensive numerical experimentation indicate strongly that computational advantages can accrue from such an approach (by comparison with “single-step” methods), particularly as the dimension of the problem increases.  相似文献   

17.
A variable-penalty alternating directions method for convex optimization   总被引:6,自引:0,他引:6  
We study a generalized version of the method of alternating directions as applied to the minimization of the sum of two convex functions subject to linear constraints. The method consists of solving consecutively in each iteration two optimization problems which contain in the objective function both Lagrangian and proximal terms. The minimizers determine the new proximal terms and a simple update of the Lagrangian terms follows. We prove a convergence theorem which extends existing results by relaxing the assumption of uniqueness of minimizers. Another novelty is that we allow penalty matrices, and these may vary per iteration. This can be beneficial in applications, since it allows additional tuning of the method to the problem and can lead to faster convergence relative to fixed penalties. As an application, we derive a decomposition scheme for block angular optimization and present computational results on a class of dual block angular problems. This material is based on research supported by the Air Force Office of Scientific Research Grant AFOSR-89-0410 and by NSF Grants CCR-8907671, CDA-9024618 and CCR-9306807.  相似文献   

18.
The Particle Swarm Optimization (PSO) method is a well-established technique for global optimization. During the past years several variations of the original PSO have been proposed in the relevant literature. Because of the increasing necessity in global optimization methods in almost all fields of science there is a great demand for efficient and fast implementations of relative algorithms. In this work we propose three modifications of the original PSO method in order to increase the speed and its efficiency that can be applied independently in almost every PSO variant. These modifications are: (a) a new stopping rule, (b) a similarity check and (c) a conditional application of some local search method. The proposed were tested using three popular PSO variants and a variety test functions. We have found that the application of these modifications resulted in significant gain in speed and efficiency.  相似文献   

19.
The purpose of this paper is to present a new method to design exact geometric predicates in algorithms dealing with curved objects such as circular arcs. We focus on the comparison of the abscissae of two intersection points of circle arcs, which is known to be a difficult predicate involved in the computation of arrangements of circle arcs. We present an algorithm for deciding the x-order of intersections from the signs of the coefficients of a polynomial, obtained by a general approach based on resultants. This method allows the use of efficient arithmetic and filtering techniques leading to fast implementation as shown by the experimental results.  相似文献   

20.
Data level parallelism is a type of parallelism whereby operations are performed on many data elements concurrently, by many processors. These operations are (more or less) identical, and are executed in a synchronous, orderly fashion. This type of parallelism is used by massively parallel SIMD (i.e., Single Instruction, Multiple Data) architectures, like the Connection Machine CM-2, the AMT DAP and Masspar, and MIMD (i.e., Multiple Instruction, Multiple Data) architectures, like the Connection Machine CM-5. Data parallelism can also be described by a theoretical model of computation: the Vector-Random Access Machine (V-RAM).In this paper we discuss practical approaches to the data-parallel solution of large scale optimization problems with network—or embedded-network—structures. The following issues are addressed: (1) The concept of dataparallelism, (2) algorithmic principles that lead to data-parallel decomposition of optimization problems with network—or embedded-network—structures, (3) specific algorithms for several network problems, (4) data-structures needed for efficient implementations of the algorithms, and (5) empirical results that highlight the performance of the algorithms on a data-parallel computer, the Connection Machine CM-2.  相似文献   

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