Multi‐Block Solution Algorithm for Joint PDF Methods

A multi‐block grid (MBG) based algorithm to solve the joint velocity‐frequency‐composition PDF transport equation for turbulent reactive flow is presented. The algorithm is based on a previously developed hybrid finite‐volume/particle approach which has significant advantages over stand alone particle PDF methods. It is demonstrated that the new solution method, due to the flexibility of MBGs, allows to perform simulation studies which involve very complex 3D geometries. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Lagrangian Joint PDF Approach for Turbulent Premixed Combustion

A model for premixed turbulent combustion based on a joint velocity probability density function (PDF) method and a progress variable is presented. Compared with other methods employing progress variables, the advantage here is that turbulent mixing of the progress variable requires no modeling. Moreover, by applying scale separation, the Lagrangian framework allows to account for the embedded, quasi laminar flame structure in a very natural way. The numerical results presented here are based on a simple closure of the progress variable source term and it is demonstrated that the new modeling approach is robust and shows the correct qualitative behavior. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Geometric Space-Time Multigrid Algorithm for the Heat Equation

We study the time-dependent heat equation on its space-time domain that is discretised by a $k$-spacetree. $k$-spacetrees are a generalisation of the octree concept and are a discretisation paradigm yielding a multiscale representation of dynamically adaptive Cartesian grids with low memory footprint. The paper presents a full approximation storage geometric multigrid implementation for this setting that combines the smoothing properties of multigrid for the equation's elliptic operator with a multiscale solution propagation in time. While the runtime and memory overhead for tackling the all-in-one space-time problem is bounded, the holistic approach promises to exhibit a better parallel scalability than classical time stepping, adaptive dynamic refinement in space and time fall naturally into place, as well as the treatment of periodic boundary conditions of steady cycle systems, on-time computational steering is eased as the algorithm delivers guesses for the solution's long-term behaviour immediately, and, finally, backward problems arising from the adjoint equation benefit from the the solution being available for any point in space and time.     

A Multigrid Block LU-SGS Algorithm for Euler Equations on Unstructured Grids

We propose an efficient and robust algorithm to solve the steady Euler equa- tions on unstructured grids.The new algorithm is a Newton-iteration method in which each iteration step is a linear multigrid method using block lower-upper symmetric Gauss-Seidel(LU-SGS)iteration as its smoother To regularize the Jacobian matrix of Newton-iteration,we adopted a local residual dependent regularization as the replace- ment of the standard time-stepping relaxation technique based on the local CFL number The proposed method can be extended to high order approximations and three spatial dimensions in a nature way.The solver was tested on a sequence of benchmark prob- lems on both quasi-uniform and local adaptive meshes.The numerical results illustrated the efficiency and robustness of our algorithm.     

A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians

In this paper, we develop a cascadic multigrid algorithm for fast computation of the Fiedler vector of a graph Laplacian, namely, the eigenvector corresponding to the second smallest eigenvalue. This vector has been found to have applications in fields such as graph partitioning and graph drawing. The algorithm is a purely algebraic approach based on a heavy edge coarsening scheme and pointwise smoothing for refinement. To gain theoretical insight, we also consider the related cascadic multigrid method in the geometric setting for elliptic eigenvalue problems and show its uniform convergence under certain assumptions. Numerical tests are presented for computing the Fiedler vector of several practical graphs, and numerical results show the efficiency and optimality of our proposed cascadic multigrid algorithm.     

Truncated Newton-Based Multigrid Algorithm for Centroidal Voronoi Diagram Calculation

In a variety of modern applications there arises a need to tessellate the domain into representative regions, called Voronoi cells. A particular type of such tessellations, called centroidal Voronoi tessellations or CVTs, are in big demand due to their optimality properties important for many applications. The availability of fast and reliable algorithms for their construction is crucial for their successful use in practical settings. This paper introduces a new multigrid algorithm for constructing CVTs that is based on the MG/Opt algorithm that was originally designed to solve large nonlinear optimization problems. Uniform convergence of the new method and its speedup comparing to existing techniques are demonstrated for linear and nonlinear densities for several 1d and 2d problems, and $O(k)$ complexity estimation is provided for a problem with $k$ generators.     

The Convergence of the Multigrid Algorithm for Navier-Stokes Equations

This paper deal with a multigrid algorithm for the numerical solution of Navier-Stokes problems. The convergence proof and estimation of the contraction number of the multigrid algorithm are given.     

带补偿C^0非协调板元的多重网格法

本文考虑重调和方程的Ｃ０非协调元逼近．通过双线性型ｃｋ（ｕ,ｖ）引入的补偿和将多重网格法应用到Ｃ０非协调板元,给出了更精确的逼近．     

复频域卷积的离散算法

导出了适用于计算机进行计算的复频域卷积的离散算法,应用Durbin拉氏变换数值反演法对复频域卷积结果进行数值反演,可获得时域数值解.将该数值解与解析解进行比较表明,数值解具有较高的精度.     

面向多目标优化的一种混合进化算法

针对多目标优化问题,设计一种基于量子计算和非支配排序遗传算法相结合的智能算法进行求解,综合量子算法和非支配排序遗传算法的优点,在局部搜索和全局搜索之间进行权衡。混合算法采用量子比特对问题的解进行编码,基于量子旋转门算子、分散交叉算子以及高斯变异算子对种群进行更新。进行局部深入搜索时,用一个解在目标空间中跟理想点的距离来评价该解的优劣;进行全局搜索时,基于非支配排序遗传算法中的有效前沿的划分和解之间的拥挤距离来评价某个解。最后,在经典的测试函数ZDT5上对所提混合算法进行了测试。通过对比分析若干项针对有效解集的评价指标,该混合算法在跟最优有效前沿的逼近程度以及有效解集分布的均匀程度上均优于目前得到广泛应用的非支配排序遗传算法。     

A Hybrid Genetic Algorithm for Assembly Line Balancing

This paper presents a hybrid genetic algorithm for the simple assembly line problem, SALBP-1. The chromosome representation of the problem is based on random keys. The assignment of the operations to the workstations is based on a heuristic priority rule in which the priorities of the operations are defined by the chromosomes. A local search is used to improve the solution. The approach is tested on a set of problems taken from the literature and compared with other approaches. The computation results validate the effectiveness of the algorithm.     

A Hybrid Genetic Algorithm for Nonconvex Function Minimization

In this paper, we consider the problem of minimizing a function in severalvariables which could be multimodal and may possess discontinuities. A newalgorithm for the problem based on the genetic technique is developed. Thealgorithm is hybrid in nature in the sense that it utilizes the genetictechnique to generate search directions, which are used in an optimizationscheme and is thus different from any other methods in the literature.The algorithm has been tested on the Rosenbrock valley functions in 2 and 4dimensions, and multimodal functions in 2 and 4 dimensions, which are of ahigh degree of difficulty. The results are compared with the Adaptive RandomSearch, and Simulated Annealing algorithms. The performance of the algorithmis also compared to recent global algorithms in terms of the number offunctional evaluations needed to obtain a global minimum and results show thatthe proposed algorithm is better than these algorithms on a set of standardtest problems. It seems that the proposed algorithm is efficient and robust.     

A Hybrid Algorithm for the Non-Guillotine Cutting Problem

In this article, a meta-heuristic method to solve the non-guillotine cutting stock problem is proposed. The method is based on a combination between the basic principles of the constructive and evolutive methods. With an adequate management of the parameters involved, the method allows regulation of the solution quality to computational effort relationship. This method is applied to a particular case of cutting problems, with which the computational behaviors is evaluated. In fact, 1000 instances of the problem have been classified according to their combinatorial degree and then the efficiency and robustness of the method have been tested. The final results conclude that the proposed method generates an average error close to 2.18% with respect to optimal solutions. It has also been verified that the method yields solutions for all of the instances examined; something that has not been achieved with an exact constructive method, which was also implemented. Comparison of the running times demonstrates the superiority of the proposed method as compared with the exact method.     

半线性问题的瀑布型多重网格法

本文提出了求解半线性椭圆问题的一类新的瀑布型多重网格法，在网格层数固定的条件下证明了此法的最优阶收敛性。     

A Multigrid Method for Nonlinear Parabolic Problems

1.IntroductionThefiniteelementmethodsforsolvingnonlinearparabolicproblemsarestudiedbymanyauthors,suchasDouglasandDupont[5],Wheelerl4],Luskin[3lfetc.Theyproposedvariouswaysofcomputingtheproblemsandprovedtheoptimalorderconvergenceratesofthemethods,suchasthelinearizedmethods,thepredictor-correctormethods,theextraPolationmethods,thealternatingdirectiollmethodsandtheiterativemethodsl2]1etc.Themultigridmethodsforsolvingparabolicproblemsarestudiedbysomeauthors,suchasHachbuschl14,15],BankandDupontl…     

A New Optimal Algorithm for the Joint Replenishment Problem

In this paper, we propose a new optimal algorithm for the Joint Replenishment Problem. The proposed algorithm can be used to determine the optimal strict-cyclic policy, as well as the optimal among all cyclic policies for the joint replenishment problem. Computational experiments on randomly generated problems reveal that the proposed algorithm performs better than existing optimal algorithms for the problem.     

MEMS矢量水听器的一种新的联合去噪算法

针对传感器水声信号存在随机噪声的问题,提出了一种正余弦算法(SCA)和粒子群算法(PSO)相结合优化变分模态分解(VMD)参数κ和α,将含噪信号通过VMD分解为k个固有模态函数,选取相关系数高的模态分量进行小波阈值(WT)去噪后重构信号分量,得到目标信号的算法,记为SCA-PSO-VMD-WT算法.通过将本算法与VMD...     

解抛物问题的一类新的瀑布型多重网格法

本文推广石钟兹 ,许学军对椭圆问题提出的新的瀑布型多重网格法到抛物问题 ,建立了相应的理论结果 .     

A Flux Correction Multigrid for Compressible Flow

A finite-volume based linear multigrid algorithm is proposed and used within an implicit linearized scheme to solve Navier–Stokes equations for compressible laminar flows. Coarse level problems are constructed algebraically based on convective and diffusive fluxes, without the knowledge of coarse geometry. Numerical results for complex 2D geometries such as airfoils, including stretched meshes, show mesh size independent convergence and efficiency of the method compared to other finite-volume-based multigrid method.