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Fast Convergence (fast + convergence)
Selected AbstractsIsotropic Remeshing with Fast and Exact Computation of Restricted Voronoi DiagramCOMPUTER GRAPHICS FORUM, Issue 5 2009Dong-Ming Yan Abstract We propose a new isotropic remeshing method, based on Centroidal Voronoi Tessellation (CVT). Constructing CVT requires to repeatedly compute Restricted Voronoi Diagram (RVD), defined as the intersection between a 3D Voronoi diagram and an input mesh surface. Existing methods use some approximations of RVD. In this paper, we introduce an efficient algorithm that computes RVD exactly and robustly. As a consequence, we achieve better remeshing quality than approximation-based approaches, without sacrificing efficiency. Our method for RVD computation uses a simple procedure and a kd -tree to quickly identify and compute the intersection of each triangle face with its incident Voronoi cells. Its time complexity is O(mlog n), where n is the number of seed points and m is the number of triangles of the input mesh. Fast convergence of CVT is achieved using a quasi-Newton method, which proved much faster than Lloyd's iteration. Examples are presented to demonstrate the better quality of remeshing results with our method than with the state-of-art approaches. [source] Adaptive finite element computation of dielectric and mechanical intensity factors in piezoelectrics with impermeable cracksINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010Abstract The paper deals with the application of an adaptive, hierarchic-iterative finite element technique to solve two-dimensional electromechanical boundary value problems with impermeable cracks in piezoelectric plates. In order to compute the dielectric and mechanical intensity factors, the interaction integral technique is used. The iterative finite element solver takes advantage of a sequence of solutions on hierarchic discretizations. Based on an a posteriori error estimation, the finite element mesh is locally refined or coarsened in each step. Two crack configurations are investigated in an infinite piezoelectric plate: A finite straight crack and a finite kinked crack. Fast convergence of the numerical intensity factors to the corresponding analytical solution is exemplarily proved during successive adaptive steps for the first configuration. Similar tendency can be observed for the second configuration. Furthermore, the computed intensity factors for the kinks are found to coincide well with the corresponding analytical values. In order to simulate the kinks spreading from a straight crack, the finite element mesh is modified automatically with a specially developed algorithm. This forms the basis for a fully adaptive simulation of crack propagation. Copyright © 2009 John Wiley & Sons, Ltd. [source] Convergence in Structure and Productivity in European Manufacturing?GERMAN ECONOMIC REVIEW, Issue 1 2004Klaus Gugler Structural convergence; productivity convergence; growth of industries; European integration Abstract. We find fast convergence in productivity for 99 three-digit European industries over the 1985,98 period. Half of any productivity gap is closed on average in about 10,15 years. We explicitly formulate the steady-state assumptions for structural convergence to hold. Convergence in industrial structure is much slower than productivity catch-up with a half-life of around 50 years, a stylized fact which cannot easily be explained by the existing models of trade and growth. [source] Static reanalysis of structures with added degrees of freedomINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2006Baisheng Wu Abstract This paper deals with static reanalysis of a structure with added degrees of freedom where the nodes of the original structure form a subset of the nodes of the modified structure. A preconditioned conjugate-gradient approach is developed. The preconditioner is constructed, and the implementation of the approach involves only decomposition of the stiffness matrix corresponding to the newly added degrees of freedom. In particular, the approach can adaptively monitor the accuracy of approximate solutions. The approach is applicable to the reanalysis of the structural layout modifications for the case of addition of some nodes, deletion and addition of elements and further changes in the geometry as well as to the local mesh refinements. Numerical examples show that the condition number of the selected preconditioned matrix is largely reduced. Therefore, the fast convergence and accurate results can be achieved by the approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] On a multilevel preconditioning module for unstructured mesh Krylov solvers: two-level SchwarzINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2002R. S. Tuminaro Abstract Multilevel methods offer the best promise to attain both fast convergence and parallel efficiency in the numerical solution of parabolic and elliptic partial differential equations. Unfortunately, they have not been widely used in part because of implementation difficulties for unstructured mesh solvers. To facilitate use, a multilevel preconditioner software module, ML, has been constructed. Several methods are provided requiring relatively modest programming effort on the part of the application developer. This report discusses the implementation of one method in the module: a two-level Krylov,Schwarz preconditioner. To illustrate the use of these methods in computational fluid dynamics (CFD) engineering applications, we present results for 2D and 3D CFD benchmark problems. Copyright © 2002 John Wiley & Sons, Ltd. [source] An appropriate quadrature rule for the analysis of plane crack problems in the boundary-element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2001E. E. Theotokoglou Abstract An hypersingular integral equation of a three-dimensional elastic solid with an embedded planar crack subjected to a uniform stress field at infinity is derived. The solution of the boundary-integral equation is succeeded taking into consideration an appropriate Gauss quadrature rule for finite part integrals which is suitable for the numerical treatment of any plane crack with a smooth-contour shape and permit the fast convergence for the results. The problem of a circular and of an elliptical crack in an infinite body subjected to a uniform stress field at infinity is confronted; and the stress intensity factors are calculated. Copyright © 2001 John Wiley & Sons, Ltd. [source] A preconditioned conjugate gradient approach to structural reanalysis for general layout modificationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2007Zhengguang Li Abstract This paper presents a preconditioned conjugate gradient approach to structural static reanalysis for general layout modifications. It is suitable for all types of layout modifications, including the general case in which some original members and nodes are deleted and other new members and nodes are added concurrently. The approach is based on the preconditioned conjugate gradient technique. The preconditioner is constructed, and an efficient implementation for applying the preconditioner is presented, which requires the factorization of the stiffness matrix corresponding to the newly added degrees of freedom only. In particular, the approach can adaptively monitor the accuracy of approximate solutions. Numerical examples show that the condition number of the preconditioned matrix is remarkably reduced. Therefore, the fast convergence and accurate results can be achieved by the approach. Copyright © 2006 John Wiley & Sons, Ltd. [source] Large-scale topology optimization using preconditioned Krylov subspace methods with recyclingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2007Shun Wang Abstract The computational bottleneck of topology optimization is the solution of a large number of linear systems arising in the finite element analysis. We propose fast iterative solvers for large three-dimensional topology optimization problems to address this problem. Since the linear systems in the sequence of optimization steps change slowly from one step to the next, we can significantly reduce the number of iterations and the runtime of the linear solver by recycling selected search spaces from previous linear systems. In addition, we introduce a MINRES (minimum residual method) version with recycling (and a short-term recurrence) to make recycling more efficient for symmetric problems. Furthermore, we discuss preconditioning to ensure fast convergence. We show that a proper rescaling of the linear systems reduces the huge condition numbers that typically occur in topology optimization to roughly those arising for a problem with constant density. We demonstrate the effectiveness of our solvers by solving a topology optimization problem with more than a million unknowns on a fast PC. Copyright © 2006 John Wiley & Sons, Ltd. [source] Numerical approximation of optimal control of unsteady flows using SQP and time decompositionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2004S. S. RavindranArticle first published online: 1 APR 200 Abstract In this paper, we present numerical approximations of optimal control of unsteady flow problems using sequential quadratic programming method (SQP) and time domain decomposition. The SQP method is considered superior due to its fast convergence and its ability to take advantage of existing numerical techniques for fluid flow problems. It iteratively solves a sequence of linear quadratic optimal control problems converging to the solution of the non-linear optimal control problem. The solution to the linear quadratic problem is characterized by the Karush,Kuhn,Tucker (KKT) optimality system which in the present context is a formidable system to solve. As a remedy various time domain decompositions, inexact SQP implementations and block iterative methods to solve the KKT systems are examined. Numerical results are presented showing the efficiency and feasibility of the algorithms. Copyright © 2004 John Wiley & Sons, Ltd. [source] An optimal spectrum-balancing algorithm for digital subscriber lines based on particle swarm optimizationINTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 9 2008Meiqin Tang Abstract This paper presents a new algorithm for optimal spectrum balancing in modern digital subscriber line (DSL) systems using particle swarm optimization (PSO). In DSL, crosstalk is one of the major performance bottlenecks, therefore various dynamic spectrum management algorithms have been proposed to reduce excess crosstalks among users by dynamically optimizing transmission power spectra. In fact, the objective function in the spectrum optimization problem is always nonconcave. PSO is a new evolution algorithm based on the movement and intelligence of swarms looking for the most fertile feeding location, which can solve discontinuous, nonconvex and nonlinear problems efficiently. The proposed algorithm optimizes the weighted rate sum. These weights allow the system operator to place differing qualities of service or importance levels on each user, which makes it possible for the system to avoid the selfish-optimum. We can show that the proposed algorithm converges to the global optimal solutions. Simulation results demonstrate that our algorithm can guarantee fast convergence within a few iterations and solve the nonconvex optimization problems efficiently. Copyright © 2008 John Wiley & Sons, Ltd. [source] Measured average cell rate-based congestion avoidance schemeINTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 1 2001Hyun M. Choi Abstract Techniques for congestion control of available bit-rate (ABR) traffic in ATM (asynchronous transfer mode) networks remain an important issue. Several congestion control schemes have been proposed to adjust the cell rates of sources with a modified or mean allowed cell rate. To make these schemes work effectively in practice, the modified or mean allowed cell rate must converge under all conditions. However, it is not easy to obtain an accurate value, and an inaccurate value could result in network performance degradation such as severe oscillations and considerable unfairness. Therefore, we propose a measured average cell rate-based congestion avoidance for ABR traffic in ATM networks. The scheme has high throughput and achieves shorter queue lengths without congestion. With measured average cell rate, the scheme provides fast convergence to a start-up virtual connection (VC) and rate of equalization from different initial conditions of the sources. Thus, this scheme provides better fairness among connections. Copyright © 2001 John Wiley & Sons, Ltd. [source] Neural network-based image restoration using scaled residual with space-variant regularizationINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 6 2002E. Salari Abstract Image restoration is aimed to recover the original scene from its degraded version. This paper presents a new method for image restoration. In this technique, an evaluation function which combines a scaled residual with space-variant regularization is established and minimized using a Hopfield network to obtain a restored image from a noise corrupted and blurred image. Simulation results demonstrate that the proposed evaluation function leads to a more efficient restoration process which offers a fast convergence and improved restored image quality. © 2003 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 247,253, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10034 [source] Multiplicative random regression model for heterogeneous variance adjustment in genetic evaluation for milk yield in SimmentalJOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 3 2008M.H. Lidauer Summary A multiplicative random regression (M-RRM) test-day (TD) model was used to analyse daily milk yields from all available parities of German and Austrian Simmental dairy cattle. The method to account for heterogeneous variance (HV) was based on the multiplicative mixed model approach of Meuwissen. The variance model for the heterogeneity parameters included a fixed region × year × month × parity effect and a random herd × test-month effect with a within-herd first-order autocorrelation between test-months. Acceleration of variance model solutions after each multiplicative model cycle enabled fast convergence of adjustment factors and reduced total computing time significantly. Maximum Likelihood estimation of within-strata residual variances was enhanced by inclusion of approximated information on loss in degrees of freedom due to estimation of location parameters. This improved heterogeneity estimates for very small herds. The multiplicative model was compared with a model that assumed homogeneous variance. Re-estimated genetic variances, based on Mendelian sampling deviations, were homogeneous for the M-RRM TD model but heterogeneous for the homogeneous random regression TD model. Accounting for HV had large effect on cow ranking but moderate effect on bull ranking. [source] Regularization and preconditioning of KKT systems arising in nonnegative least-squares problemsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2009Stefania Bellavia Abstract A regularized Newton-like method for solving nonnegative least-squares problems is proposed and analysed in this paper. A preconditioner for KKT systems arising in the method is introduced and spectral properties of the preconditioned matrix are analysed. A bound on the condition number of the preconditioned matrix is provided. The bound does not depend on the interior-point scaling matrix. Preliminary computational results confirm the effectiveness of the preconditioner and fast convergence of the iterative method established by the analysis performed in this paper. Copyright © 2008 John Wiley & Sons, Ltd. [source] Spectral analysis of parallel incomplete factorizations with implicit pseudo-overlapNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2002M. Magolu monga Made Abstract Two general parallel incomplete factorization strategies are investigated. The techniques may be interpreted as generalized domain decomposition methods. In contrast to classical domain decomposition methods, adjacent subdomains exchange data during the construction of the incomplete factorization matrix, as well as during each local forward elimination and each local backward elimination involved in the application of the preconditioner. Local renumberings of nodes are combined with suitable global fill-in strategy in an (successful) attempt to overcome the well-known trade-off between high parallelism (locality) and fast convergence (globality). From an algebraic viewpoint, our techniques may be implemented as global renumbering strategies. Theoretical spectral analysis is provided, which displays that the convergence rate weakly depends on the number of subdomains. Numerical results obtained on a 16-processor SGI Origin 2000 are reported, showing the efficiency of our parallel preconditionings. Copyright © 2001 John Wiley & Sons, Ltd. [source] Convergence acceleration by varying time-step size using Bi-CGSTAB method for turbulent flow computationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2001W. B. Tsai Abstract A design of varying step size approach both in time span and spatial coordinate systems to achieve fast convergence is demonstrated in this study. This method is based on the concept of minimization of residuals by the Bi-CGSTAB algorithm, so that the convergence can be enforced by varying the time-step size. The numerical results show that the time-step size determined by the proposed method improves the convergence rate for turbulent computations using advanced turbulence models in low Reynolds-number form, and the degree of improvement increases with the degree of the complexity of the turbulence models. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 454,474, 2001. [source] Convergence study of a Schrödinger-equation algorithm and structure-factor determination from the wavefunctionACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2008Kostas Bethanis The algorithm [Bethanis, Tzamalis, Hountas & Tsoucaris (2002). Acta Cryst. A58, 265,269] which reformulates the quantum-mechanical problem of solving a Schrödinger (S) equation in a crystallographic context has been upgraded and tested for many aspects of convergence. The upgraded algorithm in reciprocal space aims at determining a wavefunction ,H such that (a) ,H fulfils the S equation within certain precision and (b) ,H minimizes by least squares the differences between the calculated structure factors from the wavefunction and the observed ones. Calculations have been made with three molecules (11, 41 and 110 non-H atoms in the asymmetric unit) for different numbers of initially given phases. Three main questions have been addressed: (I) Does the iterative calculation of the wavefunction converge? (II) Do the calculated wavefunctions converge to a unique set of ,H values independent of the initial random set of ,H? (III) Is the calculated ,H set a good approximation of a wavefunction able to produce within certain errors the correct values of the phases of the structure factors? Concerning questions (I) and (II), our results give a strong hint about fast convergence to a unique wavefunction independent of the arbitrary starting wavefunction. This is an essential prerequisite for practical applications. For question (III) in the case closer to the ab initio situation, the final mean phase error, respectively, for the three structures is 3, 26 and 28°. The combination of (a) and (b) in the upgraded algorithm has been proved crucial especially for the results concerning the larger structures. [source] State estimation of a solid-state polymerization reactor for PET based on improved SR-UKFASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 2 2010Ji Liu Abstract A state estimator for the continuous solid-state polymerization (SSP) reactor of polyethylene terephthalate (PET) is designed in this study. Because of its invalidity in the application to some of the practical examples such as SSP processes, the square-root unscented Kalman filter (SR-UKF) algorithm is improved for the state estimation of arbitrary nonlinear systems with linear measurements. Discussions are given on how to avoid the filter invalidation and accumulating additional error. Orthogonal collocation method has been used to spatially discretize the reactor model described by nonlinear partial differential equations. The reactant concentrations on chosen collocation points are reconstructed from the outlet measurements corrupted with a large noise. Furthermore, the error performance of the developed ISR-UKF is investigated under the influence of various initial parameters, inaccurate measurement noise parameters and model mismatch. Simulation results show that this technique can produce fast convergence and good approximations for the state estimation of SSP reactor. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd. [source] Maximizing power production in a stack of microbial fuel cells using multiunit optimization methodBIOTECHNOLOGY PROGRESS, Issue 3 2009Lyne Woodward Abstract This study demonstrates real-time maximization of power production in a stack of two continuous flow microbial fuel cells (MFCs). To maximize power output, external resistances of two air,cathode membraneless MFCs were controlled by a multiunit optimization algorithm. Multiunit optimization is a recently proposed method that uses multiple similar units to optimize process performance. The experiment demonstrated fast convergence toward optimal external resistance and algorithm stability during external perturbations (e.g., temperature variations). Rate of the algorithm convergence was much faster than in traditional maximum power point tracking algorithms (MPPT), which are based on temporal perturbations. A power output of 81,84 mW/LA (A = anode volume) was achieved in each MFC. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009 [source] | |||||||||||||||||||