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Convergence Rate (convergence + rate)
Kinds of Convergence Rate Selected AbstractsJoint additive Kullback,Leibler residual minimization and regularization for linear inverse problemsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2007Elena Resmerita Abstract For the approximate solution of ill-posed inverse problems, the formulation of a regularization functional involves two separate decisions: the choice of the residual minimizer and the choice of the regularizor. In this paper, the Kullback,Leibler functional is used for both. The resulting regularization method can solve problems for which the operator and the observational data are positive along with the solution, as occur in many inverse problem applications. Here, existence, uniqueness, convergence and stability for the regularization approximations are established under quite natural regularity conditions. Convergence rates are obtained by using an a priori strategy. Copyright © 2007 John Wiley & Sons, Ltd. [source] Convergence rates toward the travelling waves for a model system of the radiating gasMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2007Masataka Nishikawa Abstract The present paper is concerned with an asymptotics of a solution to the model system of radiating gas. The previous researches have shown that the solution converges to a travelling wave with a rate (1 + t),1/4 as time t tends to infinity provided that an initial data is given by a small perturbation from the travelling wave in the suitable Sobolev space and the perturbation is integrable. In this paper, we make more elaborate analysis under suitable assumptions on initial data in order to obtain shaper convergence rates than previous researches. The first result is that if the initial data decays at the spatial asymptotic point with a certain algebraic rate, then this rate reflects the time asymptotic convergence rate. Precisely, this convergence rate is completely same as the spatial convergence rate of the initial perturbation. The second result is that if the initial data is given by the Riemann data, an admissible weak solution, which has a discontinuity, converges to the travelling wave exponentially fast. Both of two results are proved by obtaining decay estimates in time through energy methods with suitably chosen weight functions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Dynamic Wavelet Neural Network for Nonlinear Identification of Highrise BuildingsCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 5 2005Xiaomo Jiang Compared with conventional neural networks, training of a dynamic neural network for system identification of large-scale structures is substantially more complicated and time consuming because both input and output of the network are not single valued but involve thousands of time steps. In this article, an adaptive Levenberg,Marquardt least-squares algorithm with a backtracking inexact linear search scheme is presented for training of the dynamic fuzzy WNN model. The approach avoids the second-order differentiation required in the Gauss,Newton algorithm and overcomes the numerical instabilities encountered in the steepest descent algorithm with improved learning convergence rate and high computational efficiency. The model is applied to two highrise moment-resisting building structures, taking into account their geometric nonlinearities. Validation results demonstrate that the new methodology provides an efficient and accurate tool for nonlinear system identification of high-rising buildings. [source] Hybrid Meta-Heuristic Algorithm for the Simultaneous Optimization of the O,D Trip Matrix EstimationCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 6 2004Antony Stathopoulos These include a genetic algorithm (GA), a simulated annealing (SA) algorithm, and a hybrid algorithm (GASA) based on the combination of GA and SA. The computational performance of the three algorithms is evaluated and compared by implementing them on a realistic urban road network. The results of the simulation tests demonstrate that SA and GASA produce a more accurate final solution than GA, whereas GASA shows a superior convergence rate, that is, faster improvement from the initial solution, in comparison to SA and GA. In addition, GASA produces a final solution that is more robust and less dependent on the initial demand pattern, in comparison to that obtained from a greedy search algorithm. [source] A parallel multigrid solver for high-frequency electromagnetic field analyses with small-scale PC clusterELECTRONICS & COMMUNICATIONS IN JAPAN, Issue 9 2008Kuniaki Yosui Abstract Finite element analyses of electromagnetic fields are commonly used for designing various electronic devices. The scale of the analyses becomes larger and larger, therefore, a fast linear solver is needed to solve linear equations arising from the finite element method. Since a multigrid solver is the fastest linear solver for these problems, parallelization of a multigrid solver is quite a useful approach. From the viewpoint of industrial applications, an effective usage of a small-scale PC cluster is important due to initial cost for introducing parallel computers. In this paper, a distributed parallel multigrid solver for a small-scale PC cluster is developed. In high-frequency electromagnetic analyses, a special block Gauss, Seidel smoother is used for the multigrid solver instead of general smoothers such as a Gauss, Seidel or Jacobi smoother in order to improve the convergence rate. The block multicolor ordering technique is applied to parallelize the smoother. A numerical example shows that a 3.7-fold speed-up in computational time and a 3.0-fold increase in the scale of the analysis were attained when the number of CPUs was increased from one to five. © 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 91(9): 28, 36, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10160 [source] The tectonic regime along the Andes: Present-day and Mesozoic regimesGEOLOGICAL JOURNAL, Issue 1 2010Victor A. Ramos Abstract The analyses of the main parameters controlling the present Chile-type and Marianas-type tectonic settings developed along the eastern Pacific region show four different tectonic regimes: (1) a nearly neutral regime in the Oregon subduction zone; (2) major extensional regimes as the Nicaragua subduction zone developed in continental crust; (3) a Marianas setting in the Sandwich subduction zone with ocean floored back-arc basin with a unique west-dipping subduction zone and (4) the classic and dominant Chile-type under compression. The magmatic, structural and sedimentary behaviours of these four settings are discussed to understand the past tectonic regimes in the Mesozoic Andes based on their present geological and tectonic characteristics. The evaluation of the different parameters that governed the past and present tectonic regimes indicates that absolute motion of the upper plate relative to the hotspot frame and the consequent trench roll-back velocity are the first order parameters that control the deformation. Locally, the influences of the trench fill, linked to the dominant climate in the forearc, and the age of the subducted oceanic crust, have secondary roles. Ridge collisions of seismic and seismic oceanic ridges as well as fracture zone collisions have also a local outcome, and may produce an increase in coupling that reinforces compressional deformation. Local strain variations in the past and present Andes are not related with changes in the relative convergence rate, which is less important than the absolute motion relative to the Pacific hotspot frame, or changes in the thermal state of the upper plate. Changes in the slab dip, mainly those linked to steepening subduction zones, produce significant variations in the thermal state, that are important to generate extreme deformation in the foreland. Copyright © 2009 John Wiley & Sons, Ltd. [source] SEMINONPARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION OF CONDITIONAL MOMENT RESTRICTION MODELS,INTERNATIONAL ECONOMIC REVIEW, Issue 4 2007Chunrong Ai This article studies estimation of a conditional moment restriction model with the seminonparametric maximum likelihood approach proposed by Gallant and Nychka (Econometrica 55 (March 1987), 363,90). Under some sufficient conditions, we show that the estimator of the finite dimensional parameter , is asymptotically normally distributed and attains the semiparametric efficiency bound and that the estimator of the density function is consistent under L2 norm. Some results on the convergence rate of the estimated density function are derived. An easy to compute covariance matrix for the asymptotic covariance of the , estimator is presented. [source] Direct, partitioned and projected solution to finite element consolidation modelsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2002Giuseppe Gambolati Abstract Direct, partitioned, and projected (conjugate gradient-like) solution approaches are compared on unsymmetric indefinite systems arising from the finite element integration of coupled consolidation equations. The direct method is used in its most recent and computationally efficient implementations of the Harwell Software Library. The partitioned approach designed for coupled problems is especially attractive as it addresses two separate positive definite problems of a smaller size that can be solved by symmetric conjugate gradients. However, it may stagnate and when converging it does not prove competitive with a global projection method such as Bi-CGSTAB, which may take full advantage of its flexibility in working on scaled and reordered equations, and thus may greatly improve its computational performance in terms of both robustness and convergence rate. The Bi-CGSTAB superiority to the other approaches is discussed and demonstrated with a few representative examples in two-dimensional (2-D) and three-dimensional (3-D) coupled consolidation problems. Copyright © 2002 John Wiley & Sons, Ltd. [source] A simplified method for lateral response analysis of suspension bridges under wind loadsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2006Jin Cheng Abstract A simplified method for analysing lateral response of suspension bridges under wind loads is proposed in this paper. The geometric non-linearity in the deflection theory and the three components of displacement-dependent wind loads are taken into account in the method. The analytical formulas for calculating the torsional, vertical, and lateral responses of suspension bridges under wind loads are derived. An iterative procedure, which has a high convergence rate for solving the problem, is developed. The proposed method is sufficient and simple to use. Wind-induced lateral response analysis of a long-span suspension bridge demonstrates the proposed method's efficiency and accuracy. Copyright © 2006 John Wiley & Sons, Ltd. [source] FLEXMG: A new library of multigrid preconditioners for a spectral/finite element incompressible flow solverINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010M. Rasquin Abstract A new library called FLEXMG has been developed for a spectral/finite element incompressible flow solver called SFELES. FLEXMG allows the use of various types of iterative solvers preconditioned by algebraic multigrid methods. Two families of algebraic multigrid preconditioners have been implemented, namely smooth aggregation-type and non-nested finite element-type. Unlike pure gridless multigrid, both of these families use the information contained in the initial fine mesh. A hierarchy of coarse meshes is also needed for the non-nested finite element-type multigrid so that our approaches can be considered as hybrid. Our aggregation-type multigrid is smoothed with either a constant or a linear least-square fitting function, whereas the non-nested finite element-type multigrid is already smooth by construction. All these multigrid preconditioners are tested as stand-alone solvers or coupled with a GMRES method. After analyzing the accuracy of the solutions obtained with our solvers on a typical test case in fluid mechanics, their performance in terms of convergence rate, computational speed and memory consumption is compared with the performance of a direct sparse LU solver as a reference. Finally, the importance of using smooth interpolation operators is also underlined in the study. Copyright © 2010 John Wiley & Sons, Ltd. [source] A Cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2010Phong B. H. Le Abstract In this paper, high-order systems are reformulated as first-order systems, which are then numerically solved by a collocation method. The collocation method is based on Cartesian discretization with 1D-integrated radial basis function networks (1D-IRBFN) (Numer. Meth. Partial Differential Equations 2007; 23:1192,1210). The present method is enhanced by a new boundary interpolation technique based on 1D-IRBFN, which is introduced to obtain variable approximation at irregular points in irregular domains. The proposed method is well suited to problems with mixed boundary conditions on both regular and irregular domains. The main results obtained are (a) the boundary conditions for the reformulated problem are of Dirichlet type only; (b) the integrated RBFN approximation avoids the well-known reduction of convergence rate associated with differential formulations; (c) the primary variable (e.g. displacement, temperature) and the dual variable (e.g. stress, temperature gradient) have similar convergence order; (d) the volumetric locking effects associated with incompressible materials in solid mechanics are alleviated. Numerical experiments show that the proposed method achieves very good accuracy and high convergence rates. Copyright © 2009 John Wiley & Sons, Ltd. [source] A corrected XFEM approximation without problems in blending elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008Thomas-Peter Fries Abstract The extended finite element method (XFEM) enables local enrichments of approximation spaces. Standard finite elements are used in the major part of the domain and enriched elements are employed where special solution properties such as discontinuities and singularities shall be captured. In elements that blend the enriched areas with the rest of the domain problems arise in general. These blending elements often require a special treatment in order to avoid a decrease in the overall convergence rate. A modification of the XFEM approximation is proposed in this work. The enrichment functions are modified such that they are zero in the standard elements, unchanged in the elements with all their nodes being enriched, and varying continuously in the blending elements. All nodes in the blending elements are enriched. The modified enrichment function can be reproduced exactly everywhere in the domain and no problems arise in the blending elements. The corrected XFEM is applied to problems in linear elasticity and optimal convergence rates are achieved. Copyright © 2007 John Wiley & Sons, Ltd. [source] Smooth finite element methods: Convergence, accuracy and propertiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2008Hung Nguyen-Xuan Abstract A stabilized conforming nodal integration finite element method based on strain smoothing stabilization is presented. The integration of the stiffness matrix is performed on the boundaries of the finite elements. A rigorous variational framework based on the Hu,Washizu assumed strain variational form is developed. We prove that solutions yielded by the proposed method are in a space bounded by the standard, finite element solution (infinite number of subcells) and a quasi-equilibrium finite element solution (a single subcell). We show elsewhere the equivalence of the one-subcell element with a quasi-equilibrium finite element, leading to a global a posteriori error estimate. We apply the method to compressible and incompressible linear elasticity problems. The method can always achieve higher accuracy and convergence rates than the standard finite element method, especially in the presence of incompressibility, singularities or distorted meshes, for a slightly smaller computational cost. It is shown numerically that the one-cell smoothed four-noded quadrilateral finite element has a convergence rate of 2.0 in the energy norm for problems with smooth solutions, which is remarkable. For problems with rough solutions, this element always converges faster than the standard finite element and is free of volumetric locking without any modification of integration scheme. Copyright © 2007 John Wiley & Sons, Ltd. [source] Locking-free finite elements for shear deformable orthotropic thin-walled beamsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2007F. Minghini Abstract Numerical models for finite element analyses of assemblages of thin-walled open-section profiles are presented. The assumed kinematical model is based on Timoshenko,Reissner theory so as to take shear strain effects of non-uniform bending and torsion into account. Hence, strain elastic-energy coupling terms arise between bending in the two principal planes and between bending and torsion. The adopted model holds for both isotropic and orthotropic beams. Several displacement interpolation fields are compared with the available numerical examples. In particular, some shape functions are obtained from ,modified' Hermitian polynomials that produce a locking-free Timoshenko beam element. Analogously, numerical interpolation for torsional rotation and cross-section warping are proposed resorting to one Hermitian and six Lagrangian formulation. Analyses of beams with mono-symmetric and non-symmetric cross-sections are performed to verify convergence rate and accuracy of the proposed formulations, especially in the presence of coupling terms due to shear deformations, pointing out the decay length of end effects. Profiles made of both isotropic and fibre-reinforced plastic materials are considered. The presented beam models are compared with results given by plate-shell models. Copyright © 2007 John Wiley & Sons, Ltd. [source] Strong and weak arbitrary discontinuities in spectral finite elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2005A. Legay Abstract Methods for constructing arbitrary discontinuities within spectral finite elements are described and studied. We use the concept of the eXtended Finite Element Method (XFEM), which introduces the discontinuity through a local partition of unity, so there is no requirement for the mesh to be aligned with the discontinuities. A key aspect of the implementation of this method is the treatment of the blending elements adjacent to the local partition of unity. We found that a partition constructed from spectral functions one order lower than the continuous approximation is optimal and no special treatment is needed for higher order elements. For the quadrature of the Galerkin weak form, since the integrand is discontinuous, we use a strategy of subdividing the discontinuous elements into 6- and 10-node triangles; the order of the element depends on the order of the spectral method for curved discontinuities. Several numerical examples are solved to examine the accuracy of the methods. For straight discontinuities, we achieved the optimal convergence rate of the spectral element. For the curved discontinuity, the convergence rate in the energy norm error is suboptimal. We attribute the suboptimality to the approximations in the quadrature scheme. We also found that modification of the adjacent elements is only needed for lower order spectral elements. Copyright © 2005 John Wiley & Sons, Ltd. [source] Simple modifications for stabilization of the finite point methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005B. Boroomand Abstract A stabilized version of the finite point method (FPM) is presented. A source of instability due to the evaluation of the base function using a least square procedure is discussed. A suitable mapping is proposed and employed to eliminate the ill-conditioning effect due to directional arrangement of the points. A step by step algorithm is given for finding the local rotated axes and the dimensions of the cloud using local average spacing and inertia moments of the points distribution. It is shown that the conventional version of FPM may lead to wrong results when the proposed mapping algorithm is not used. It is shown that another source for instability and non-monotonic convergence rate in collocation methods lies in the treatment of Neumann boundary conditions. Unlike the conventional FPM, in this work the Neumann boundary conditions and the equilibrium equations appear simultaneously in a weight equation similar to that of weighted residual methods. The stabilization procedure may be considered as an interpretation of the finite calculus (FIC) method. The main difference between the two stabilization procedures lies in choosing the characteristic length in FIC and the weight of the boundary residual in the proposed method. The new approach also provides a unique definition for the sign of the stabilization terms. The reasons for using stabilization terms only at the boundaries is discussed and the two methods are compared. Several numerical examples are presented to demonstrate the performance and convergence of the proposed methods. Copyright © 2005 John Wiley & Sons, Ltd. [source] Moving kriging interpolation and element-free Galerkin methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003Lei Gu Abstract A new formulation of the element-free Galerkin (EFG) method is presented in this paper. EFG has been extensively popularized in the literature in recent years due to its flexibility and high convergence rate in solving boundary value problems. However, accurate imposition of essential boundary conditions in the EFG method often presents difficulties because the Kronecker delta property, which is satisfied by finite element shape functions, does not necessarily hold for the EFG shape function. The proposed new formulation of EFG eliminates this shortcoming through the moving kriging (MK) interpolation. Two major properties of the MK interpolation: the Kronecker delta property (,I(sJ)=,IJ) and the consistency property (,In,I(x)=1 and ,In,I(x)xIi=xi) are proved. Some preliminary numerical results are given. Copyright © 2002 John Wiley & Sons, Ltd. [source] Surface wavelets: a multiresolution signal processing tool for 3D computational modellingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2001Kevin Amaratunga Abstract In this paper, we provide an introduction to wavelet representations for complex surfaces (surface wavelets), with the goal of demonstrating their potential for 3D scientific and engineering computing applications. Surface wavelets were originally developed for representing geometric objects in a multiresolution format in computer graphics. These wavelets share all of the major advantages of conventional wavelets, in that they provide an analysis tool for studying data, functions and operators at different scales. However, unlike conventional wavelets, which are restricted to uniform grids, surface wavelets have the power to perform signal processing operations on complex meshes, such as those encountered in finite element modelling. This motivates the study of surface wavelets as an efficient representation for the modelling and simulation of physical processes. We show how surface wavelets can be applied to partial differential equations, stated either in integral form or in differential form. We analyse and implement the wavelet approach for a model 3D potential problem using a surface wavelet basis with linear interpolating properties. We show both theoretically and experimentally that an O(h) convergence rate, hn being the mesh size, can be obtained by retaining only O((logN) 7/2N) entries in the discrete operator matrix, where N is the number of unknowns. The principles described here may also be extended to volumetric discretizations. Copyright © 2001 John Wiley & Sons, Ltd. [source] Performance analysis of IDEAL algorithm for three-dimensional incompressible fluid flow and heat transfer problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2009Dong-Liang Sun Abstract Recently, an efficient segregated algorithm for incompressible fluid flow and heat transfer problems, called inner doubly iterative efficient algorithm for linked equations (IDEAL), has been proposed by the present authors. In the algorithm there exist inner doubly iterative processes for pressure equation at each iteration level, which almost completely overcome two approximations in SIMPLE algorithm. Thus, the coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of solution process. However, validations have only been conducted for two-dimensional cases. In the present paper the performance of the IDEAL algorithm for three-dimensional incompressible fluid flow and heat transfer problems is analyzed and a systemic comparison is made between the algorithm and three other most widely used algorithms (SIMPLER, SIMPLEC and PISO). By the comparison of five application examples, it is found that the IDEAL algorithm is the most robust and the most efficient one among the four algorithms compared. For the five three-dimensional cases studied, when each algorithm works at its own optimal under-relaxation factor, the IDEAL algorithm can reduce the computation time by 12.9,52.7% over SIMPLER algorithm, by 45.3,73.4% over SIMPLEC algorithm and by 10.7,53.1% over PISO algorithm. Copyright © 2009 John Wiley & Sons, Ltd. [source] Geometrical interpretation of the multi-point flux approximation L-methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2009Yufei Cao Abstract In this paper, we first investigate the influence of different Dirichlet boundary discretizations on the convergence rate of the multi-point flux approximation (MPFA) L-method by the numerical comparisons between the MPFA O- and L-method, and show how important it is for this new method to handle Dirichlet boundary conditions in a suitable way. A new Dirichlet boundary strategy is proposed, which in some sense can well recover the superconvergence rate of the normal velocity. In the second part of the work, the MPFA L-method with homogeneous media is studied. A systematic concept and geometrical interpretations of the L-method are given and illustrated, which yield more insight into the L-method. Finally, we apply the MPFA L-method for two-phase flow in porous media on different quadrilateral grids and compare its numerical results for the pressure and saturation with the results of the two-point flux approximation method. Copyright © 2008 John Wiley & Sons, Ltd. [source] A reduced-order simulated annealing approach for four-dimensional variational data assimilation in meteorology and oceanographyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2008I. Hoteit Abstract Four-dimensional variational data assimilation in meteorology and oceanography suffers from the presence of local minima in the cost function. These local minima arise when the system under study is strongly nonlinear. The number of local minima further dramatically increases with the length of the assimilation period and often renders the solution to the problem intractable. Global optimization methods are therefore needed to resolve this problem. However, the huge computational burden makes the application of these sophisticated techniques unfeasible for large variational data assimilation systems. In this study, a Simulated Annealing (SA) algorithm, complemented with an order-reduction of the control vector, is used to tackle this problem. SA is a very powerful tool of combinatorial minimization in the presence of several local minima at the cost of increasing the execution time. Order-reduction is then used to reduce the dimension of the search space in order to speed up the convergence rate of the SA algorithm. This is achieved through a proper orthogonal decomposition. The new approach was implemented with a realistic eddy-permitting configuration of the Massachusetts Institute of Technology general circulation model (MITgcm) of the tropical Pacific Ocean. Numerical results indicate that the reduced-order SA approach was able to efficiently reduce the cost function with a reasonable number of function evaluations. Copyright © 2008 John Wiley & Sons, Ltd. [source] A Cartesian grid technique based on one-dimensional integrated radial basis function networks for natural convection in concentric annuliINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008N. Mai-Duy Abstract This paper reports a radial basis function (RBF)-based Cartesian grid technique for the simulation of two-dimensional buoyancy-driven flow in concentric annuli. The continuity and momentum equations are represented in the equivalent stream function formulation that reduces the number of equations from three to one, but involves higher-order derivatives. The present technique uses a Cartesian grid to discretize the problem domain. Along a grid line, one-dimensional integrated RBF networks (1D-IRBFNs) are employed to represent the field variables. The capability of 1D-IRBFNs to handle unstructured points with accuracy is exploited to describe non-rectangular boundaries in a Cartesian grid, while the method's ability to avoid the reduction of convergence rate caused by differentiation is instrumental in improving the quality of the approximation of higher-order derivatives. The method is applied to simulate thermally driven flows in annuli between two circular cylinders and between an outer square cylinder and an inner circular cylinder. High Rayleigh number solutions are achieved and they are in good agreement with previously published numerical data. Copyright © 2007 John Wiley & Sons, Ltd. [source] Numerical methods for large-eddy simulation in general co-ordinatesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2004Gefeng Tang Abstract Large scale unsteady motions in many practical engineering flows play a very important role and it is very unlikely that these unsteady flow features can be captured within the framework of Reynolds averaged Navier,Stokes approach. Large-eddy simulation (LES) has become, arguably, the only practical numerical tool for predicting those flows more accurately since it is still not realistic to apply DNS to practical engineering flows with the current and near future available computing power. Numerical methods for the LES of turbulent flows in complex geometry have been developed and applied to predict practical engineering flows successfully. The method is based on body-fitted curvilinear co-ordinates with the contravariant velocity components of the general Navier,Stokes equations discretized on a staggered orthogonal mesh. For incompressible flow simulations the main source of computational expense is due to the solution of a Poisson equation for pressure. This is especially true for flows in complex geometry. A multigrid 3D pressure solver is developed to speed up the solution. In addition, the Poisson equation for pressure takes a simpler form with no cross-derivatives when orthogonal mesh is used and hence resulting in increased convergence rate and producing more accurate solutions. Copyright © 2004 John Wiley & Sons, Ltd. [source] Interface reconstruction with least-square fit and split Eulerian,Lagrangian advectionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003Ruben Scardovelli Abstract Two new volume-of-fluid (VOF) reconstruction algorithms, which are based on a least-square fit technique, are presented. Their performance is tested for several standard shapes and is compared to a few other VOF/PLIC reconstruction techniques, showing in general a better convergence rate. The geometric nature of Lagrangian and Eulerian split advection algorithms is investigated in detail and a new mixed split Eulerian implicit,Lagrangian explicit (EI,LE) scheme is presented. This method conserves the mass to machine error, performs better than split Eulerian and Lagrangian algorithms, and it is only slightly worse than unsplit schemes. However, the combination of the interface reconstruction with the least-square fit and its advection with the EI,LE scheme appears superior to other existing approaches. Copyright © 2003 John Wiley & Sons, Ltd. [source] Convergence acceleration by self-adjusted time stepsize using Bi-CGSTAB method for turbulent separated flow computationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2002W. B. Tsai Abstract Poor convergence behavior is usually encountered when numerical computations on turbulent separated flow are performed. A design of self-adjusted stepsize concept both in time span and spatial coordinate systems to achieve faster convergence is demonstrated in this study. The determination of the time stepsize based on the concept of minimization of residuals using the Bi-CGSTAB algorithm is proposed. The numerical results show that the time stepsize adjusted by the proposed method indeed improves the convergence rate for turbulent separated flow computations using advanced turbulence models in low-Reynolds number forms. Copyright © 2002 John Wiley & Sons, Ltd. [source] A domain decomposition method for modelling Stokes flow in porous materialsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2002Guangli Liu Abstract An algorithm is presented for solving the Stokes equation in large disordered two-dimensional porous domains. In this work, it is applied to random packings of discs, but the geometry can be essentially arbitrary. The approach includes the subdivision of the domain and a subsequent application of boundary integral equations to the subdomains. This gives a block diagonal matrix with sparse off-block components that arise from shared variables on internal subdomain boundaries. The global problem is solved using a biconjugate gradient routine with preconditioning. Results show that the effectiveness of the preconditioner is strongly affected by the subdomain structure, from which a methodology is proposed for the domain decomposition step. A minimum is observed in the solution time versus subdomain size, which is governed by the time required for preconditioning, the time for vector multiplications in the biconjugate gradient routine, the iterative convergence rate and issues related to memory allocation. The method is demonstrated on various domains including a random 1000-particle domain. The solution can be used for efficient recovery of point velocities, which is discussed in the context of stochastic modelling of solute transport. Copyright © 2002 John Wiley & Sons, Ltd. [source] Design of a near-optimal adaptive filter in digital signal processor for active noise controlINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 1 2008S. M. Yang Abstract Adaptive filter has been applied in adaptive feedback and feedforward control systems, where the filter dimension is often determined by trial-and-error. The controller design based on a near-optimal adaptive filter in digital signal processor (DSP) is developed in this paper for real-time applications. The design integrates the adaptive filter and the experimental design such that their advantages in stability and robustness can be combined. The near-optimal set of controller parameters, including the sampling rate, the dimension of system identification model, the dimension (order) of adaptive controller in the form of an FIR filter, and the convergence rate of adaptation is shown to achieve the best possible system performance. In addition, the sensitivity of each design parameter can be determined by analysis of means and analysis of variance. Effectiveness of the adaptive controller on a DSP is validated by an active noise control experiment. Copyright © 2007 John Wiley & Sons, Ltd. [source] A rapidly converging filtered-error algorithm for multichannel active noise controlINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 7 2007A. P. Berkhoff Abstract In this paper, a multichannel adaptive control algorithm is described which has good convergence properties while having relatively small computational complexity. This complexity is similar to that of the filtered-error algorithm. In order to obtain these properties, the algorithm is based on a preprocessing step for the actuator signals using a stable and causal inverse of the minimum-phase part of the transfer path between actuators and error sensors, the secondary path. The latter algorithm is known from the literature as postconditioned filtered-error algorithm, which improves convergence rate for the case that the minimum-phase part of the secondary path increases the eigenvalue spread. However, the convergence rate of this algorithm suffers from delays in the adaptation path because adaptation rates have to be reduced for larger delays. The contribution of this paper is to modify the postconditioned filtered-error scheme in such a way that the adaptation rate can be set to a higher value. Consequently, the scheme also provides good convergence if the system contains significant delays. Furthermore, a regularized extension of the scheme is given which can be used to limit the actuator signals. Copyright © 2006 John Wiley & Sons, Ltd. [source] Composite adaptive and input observer-based approaches to the cylinder flow estimation in spark ignition automotive enginesINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 2 2004A. Stotsky Abstract The performance of air charge estimation algorithms in spark ignition automotive engines can be enhanced using advanced estimation techniques available in the controls literature. This paper illustrates two approaches of this kind that can improve the cylinder flow estimation for gasoline engines without external exhaust gas recirculation (EGR). The first approach is based on an input observer, while the second approach relies on an adaptive estimator. Assuming that the cylinder flow is nominally estimated via a speed-density calculation, and that the uncertainty is additive to the volumetric efficiency, the straightforward application of an input observer provides an easy to implement algorithm that corrects the nominal air flow estimate. The experimental results that we report in the paper point to a sufficiently good transient behaviour of the estimator. The signal quality may deteriorate, however, for extremely fast transients. This motivates the development of an adaptive estimator that relies mostly on the feedforward speed-density calculation during transients, while during engine operation close to steady-state conditions, it relies mostly on the adaptation. In our derivation of the adaptive estimator, the uncertainty is modelled as an unknown parameter multiplying the intake manifold temperature. We use the tracking error between the measured and modelled intake manifold pressure together with an appropriately defined prediction error estimate to develop an adaptation algorithm with improved identifiability and convergence rate. A robustness enhancement, via a ,-modification with the ,-factor depending on the prediction error estimate, ensures that in transients the parameter estimate converges to a pre-determined a priori value. In close to steady-state conditions, the ,-modification is rendered inactive and the evolution of the parameter estimate is determined by both tracking error and prediction error estimate. Further enhancements are made by incorporating a functional dependence of the a priori value on the engine operating conditions such as the intake manifold pressure. The coefficients of this function can be learned during engine operation from the values to which the parameter estimate converges in close to steady-state conditions. This feedforward learning functionality improves transient estimation accuracy and reduces the convergence time of the parameter estimate. Copyright © 2004 John Wiley & Sons, Ltd. [source] Exponential convergence of the Kalman filter based parameter estimation algorithmINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 10 2003Liyu Cao Abstract In this paper we shall present a new method to analyse the convergence property of the Kalman filter based parameter estimation algorithms. This method for convergence analysis is mainly based on some matrix inequalities and is more simple than some of the existing approaches in the literature. This method can simultaneously provide both lower and upper bounds on the exponential convergence rate as the functions of bounds of the related matrices, such as the covariance matrices. A simulation example is provided to illustrate the convergence property of the Kalman filter based algorithms. 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