Convergence Properties (convergence + property)

Distribution by Scientific Domains
Distribution within Engineering


Selected Abstracts


Convergence properties of bias-eliminating algorithms for errors-in-variables identification

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 9 2005
Torsten Söderström
Abstract This paper considers the problem of dynamic errors-in-variables identification. Convergence properties of the previously proposed bias-eliminating algorithms are investigated. An error dynamic equation for the bias-eliminating parameter estimates is derived. It is shown that the convergence of the bias-eliminating algorithms is basically determined by the eigenvalue of largest magnitude of a system matrix in the estimation error dynamic equation. When this system matrix has all its eigenvalues well inside the unit circle, the bias-eliminating algorithms can converge fast. In order to avoid possible divergence of the iteration-type bias-eliminating algorithms in the case of high noise, the bias-eliminating problem is re-formulated as a minimization problem associated with a concentrated loss function. A variable projection algorithm is proposed to efficiently solve the resulting minimization problem. A numerical simulation study is conducted to demonstrate the theoretical analysis. Copyright © 2005 John Wiley & Sons, Ltd. [source]


Kalman filter-based adaptive control for networked systems with unknown parameters and randomly missing outputs

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 18 2009
Y. Shi
Abstract This paper investigates the problem of adaptive control for networked control systems with unknown model parameters and randomly missing outputs. In particular, for a system with the autoregressive model with exogenous input placed in a network environment, the randomly missing output feature is modeled as a Bernoulli process. Then, an output estimator is designed to online estimate the missing output measurements, and further a Kalman filter-based method is proposed for parameter estimation. Based on the estimated output and the available output, and the estimated model parameters, an adaptive control is designed to make the output track the desired signal. Convergence properties of the proposed algorithms are analyzed in detail. Simulation examples illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd. [source]


Parallel Newton two-stage methods based on ILU factorizations for nonlinear systems

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 7 2006
J. Arnal
Abstract Parallel iterative algorithms based on the Newton method and on two of its variants, the Shamanskii method and the Chord method, for solving nonlinear systems are proposed. These algorithms are based on two-stage multisplitting methods where incomplete LU factorizations are considered as a mean of constructing the inner splittings. Convergence properties of these parallel methods are studied for H -matrices. Computational results of these methods on two parallel computing systems are discussed. The reported experiments show the effectiveness of these methods. Copyright © 2006 John Wiley & Sons, Ltd. [source]


ON SOCIAL LEARNING AND ROBUST EVOLUTIONARY ALGORITHM DESIGN IN THE COURNOT OLIGOPOLY GAME

COMPUTATIONAL INTELLIGENCE, Issue 2 2007
Floortje Alkemade
Agent-based computational economics (ACE) combines elements from economics and computer science. In this article, the focus is on the relation between the evolutionary technique that is used and the economic problem that is modeled. In the field of ACE, economic simulations often derive parameter settings for the genetic algorithm directly from the values of the economic model parameters. This article compares two important approaches that are dominating in ACE and shows that the above practice may hinder the performance of the genetic algorithm and thereby hinder agent learning. More specifically, it is shown that economic model parameters and evolutionary algorithm parameters should be treated separately by comparing the two widely used approaches to social learning with respect to their convergence properties and robustness. This leads to new considerations for the methodological aspects of evolutionary algorithm design within the field of ACE. [source]


An extended finite element framework for slow-rate frictional faulting with bulk plasticity and variable friction

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2009
Fushen Liu
Abstract We present an extended finite element (FE) approach for the simulation of slow-rate frictional faulting in geologic media incorporating bulk plasticity and variable friction. The method allows the fault to pass through the interior of FEs without remeshing. The extended FE algorithm for frictional faulting, advocated in two recent articles, emanates from a variational equation formulated in terms of the relative displacement on the fault. In the present paper we consider the combined effects of bulk plasticity and variable friction in a two-dimensional plane strain setting. Bulk plasticity is localized to the fault tip and could potentially be used as a predictor for the initiation and propagation of new faults. We utilize a variable velocity- and state-dependent friction, known as the Dieterich,Ruina or ,slowness' law, formulated in a slip-weakening format. The slip-weakening/variable friction model is then time-integrated according to the generalized trapezoidal rule. We present numerical examples demonstrating the convergence properties of a global Newton-based iterative scheme, as well as illustrate some interesting properties of the variable friction model. Copyright © 2009 John Wiley & Sons, Ltd. [source]


Implicit integration of a chemo-plastic constitutive model for partially saturated soils

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2008
H. W. Zhang
Abstract A chemo-plastic constitutive model for partially saturated soils is proposed in this paper based on the existing models developed in Hueckel (Int. J. Numer. Anal. Meth. Geomech. 1997; 21:43,72) and Gallipoli et al. (Geotechnique 2003; 53:123,135). The chemical softening effects due to the increase in contaminant mass concentration are considered based on Hueckel's chemo-plastic model. Gallipoli's model is used to simulate the effects of suction and degree of saturation on mechanical behavior of partially saturated porous materials. In order to implement the proposed model in a finite element code, a fully implicit backward-Euler integration algorithm is put forward. Numerical solutions for the tests at local level and the application of the algorithm to the real boundary value problem demonstrate the accuracy and convergence properties of the proposed integration scheme. Copyright © 2008 John Wiley & Sons, Ltd. [source]


Implicit integration of a mixed isotropic,kinematic hardening plasticity model for structured clays

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2008
Angelo Amorosi
Abstract In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non-trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress-point algorithm for the numerical integration of a single-surface mixed isotropic,kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid-shaped yield function, inside which a stress-dependent reversible stiffness is accounted for by a non-linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam-Clay one to include plastic strain-driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global-level Newton,Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 John Wiley & Sons, Ltd. [source]


Smeared crack approach: back to the original track

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2006
M. Cervera
Abstract This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on the smeared approach, identifying as its main drawbacks the observed mesh-size and mesh-bias spurious dependence when the method is applied ,straightly'. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and the strong discontinuity (discrete cracks) approaches are analysed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh-size or mesh-bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches. Copyright © 2006 John Wiley & Sons, Ltd. [source]


Comparison between cohesive zone models

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2004
K. Y. Volokh
Cohesive zone models (CZMs) are widely used for numerical simulation of the fracture process. Cohesive zones are surfaces of discontinuities where displacements jump. A specific constitutive law relating the displacement jumps and proper tractions defines the cohesive zone model. Within the cohesive zone approach crack nucleation, propagation, and arrest are a natural outcome of the theory. The latter is in contrast to the traditional approach of fracture mechanics where stress analysis is separated from a description of the actual process of material failure. The common wisdom says that only cohesive strength,the maximum stress on the traction,separation curve,and the separation work,the area under the traction,separation curve,are important in setting a CZM while the shape of the traction,separation curve is subsidiary. It is shown in our note that this rule may not be correct and a specific shape of the cohesive zone model can significantly affect results of the fracture analysis. For this purpose four different cohesive zone models,bilinear, parabolic, sinusoidal, and exponential,are compared by using a block-peel test, which allows for simple analytical solutions. Numerical performance of the cohesive zone models is considered. It appears that the convergence properties of nonlinear finite element analyses are similar for all four CZMs in the case of the block-peel test. Copyright © 2004 John Wiley & Sons, Ltd. [source]


eXtended Stochastic Finite Element Method for the numerical simulation of heterogeneous materials with random material interfaces

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010
A. Nouy
Abstract An eXtended Stochastic Finite Element Method has been recently proposed for the numerical solution of partial differential equations defined on random domains. This method is based on a marriage between the eXtended Finite Element Method and spectral stochastic methods. In this article, we propose an extension of this method for the numerical simulation of random multi-phased materials. The random geometry of material interfaces is described implicitly by using random level set functions. A fixed deterministic finite element mesh, which is not conforming to the random interfaces, is then introduced in order to approximate the geometry and the solution. Classical spectral stochastic finite element approximation spaces are not able to capture the irregularities of the solution field with respect to spatial and stochastic variables, which leads to a deterioration of the accuracy and convergence properties of the approximate solution. In order to recover optimal convergence properties of the approximation, we propose an extension of the partition of unity method to the spectral stochastic framework. This technique allows the enrichment of approximation spaces with suitable functions based on an a priori knowledge of the irregularities in the solution. Numerical examples illustrate the efficiency of the proposed method and demonstrate the relevance of the enrichment procedure. Copyright © 2010 John Wiley & Sons, Ltd. [source]


Fast single domain,subdomain BEM algorithm for 3D incompressible fluid flow and heat transfer

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2009
Jure Ravnik
Abstract In this paper acceleration and computer memory reduction of an algorithm for the simulation of laminar viscous flows and heat transfer is presented. The algorithm solves the velocity,vorticity formulation of the incompressible Navier,Stokes equations in 3D. It is based on a combination of a subdomain boundary element method (BEM) and single domain BEM. The CPU time and storage requirements of the single domain BEM are reduced by implementing a fast multipole expansion method. The Laplace fundamental solution, which is used as a special weighting function in BEM, is expanded in terms of spherical harmonics. The computational domain and its boundary are recursively cut up forming a tree of clusters of boundary elements and domain cells. Data sparse representation is used in parts of the matrix, which correspond to boundary-domain clusters pairs that are admissible for expansion. Significant reduction of the complexity is achieved. The paper presents results of testing of the multipole expansion algorithm by exploring its effect on the accuracy of the solution and its influence on the non-linear convergence properties of the solver. Two 3D benchmark numerical examples are used: the lid-driven cavity and the onset of natural convection in a differentially heated enclosure. Copyright © 2008 John Wiley & Sons, Ltd. [source]


An assumed-gradient finite element method for the level set equation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2005
Hashem M. Mourad
Abstract The level set equation is a non-linear advection equation, and standard finite-element and finite-difference strategies typically employ spatial stabilization techniques to suppress spurious oscillations in the numerical solution. We recast the level set equation in a simpler form by assuming that the level set function remains a signed distance to the front/interface being captured. As with the original level set equation, the use of an extensional velocity helps maintain this signed-distance function. For some interface-evolution problems, this approach reduces the original level set equation to an ordinary differential equation that is almost trivial to solve. Further, we find that sufficient accuracy is available through a standard Galerkin formulation without any stabilization or discontinuity-capturing terms. Several numerical experiments are conducted to assess the ability of the proposed assumed-gradient level set method to capture the correct solution, particularly in the presence of discontinuities in the extensional velocity or level-set gradient. We examine the convergence properties of the method and its performance in problems where the simplified level set equation takes the form of a Hamilton,Jacobi equation with convex/non-convex Hamiltonian. Importantly, discretizations based on structured and unstructured finite-element meshes of bilinear quadrilateral and linear triangular elements are shown to perform equally well. Copyright © 2005 John Wiley & Sons, Ltd. [source]


A reproducing kernel method with nodal interpolation property

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2003
Jiun-Shyan Chen
Abstract A general formulation for developing reproducing kernel (RK) interpolation is presented. This is based on the coupling of a primitive function and an enrichment function. The primitive function introduces discrete Kronecker delta properties, while the enrichment function constitutes reproducing conditions. A necessary condition for obtaining a RK interpolation function is an orthogonality condition between the vector of enrichment functions and the vector of shifted monomial functions at the discrete points. A normalized kernel function with relative small support is employed as the primitive function. This approach does not employ a finite element shape function and therefore the interpolation function can be arbitrarily smooth. To maintain the convergence properties of the original RK approximation, a mixed interpolation is introduced. A rigorous error analysis is provided for the proposed method. Optimal order error estimates are shown for the meshfree interpolation in any Sobolev norms. Optimal order convergence is maintained when the proposed method is employed to solve one-dimensional boundary value problems. Numerical experiments are done demonstrating the theoretical error estimates. The performance of the method is illustrated in several sample problems. Copyright © 2003 John Wiley & Sons, Ltd. [source]


A volume-of-fluid method for incompressible free surface flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009
I. R. Park
Abstract This paper proposes a hybrid volume-of-fluid (VOF) level-set method for simulating incompressible two-phase flows. Motion of the free surface is represented by a VOF algorithm that uses high resolution differencing schemes to algebraically preserve both the sharpness of interface and the boundedness of volume fraction. The VOF method is specifically based on a simple order high resolution scheme lower than that of a comparable method, but still leading to a nearly equivalent order of accuracy. Retaining the mass conservation property, the hybrid algorithm couples the proposed VOF method with a level-set distancing algorithm in an implicit manner when the normal and the curvature of the interface need to be accurate for consideration of surface tension. For practical purposes, it is developed to be efficiently and easily extensible to three-dimensional applications with a minor implementation complexity. The accuracy and convergence properties of the method are verified through a wide range of tests: advection of rigid interfaces of different shapes, a three-dimensional air bubble's rising in viscous liquids, a two-dimensional dam-break, and a three-dimensional dam-break over an obstacle mounted on the bottom of a tank. The standard advection tests show that the volume advection algorithm is comparable in accuracy with geometric interface reconstruction algorithms of higher accuracy than other interface capturing-based methods found in the literature. The numerical results for the remainder of tests show a good agreement with other numerical solutions or available experimental data. Copyright © 2009 John Wiley & Sons, Ltd. [source]


Optimal convergence properties of the FETI domain decomposition method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2007
Y. Maday
Abstract In this paper an original variant of the FETI domain decomposition method is introduced for heterogeneous media. This method uses new absorbing interface conditions in place of the Neumann interface conditions defined in the classical FETI method. The optimal convergence properties of the classical FETI method and of its variant are first demonstrated, both in the case of homogeneous and heterogeneous media. Secondly, novel and efficient absorbing interface conditions, which avoid rigid body motions, are investigated and analysed. Numerical experiments illustrate the dependence of the proposed method upon several parameters, and confirm the robustness and efficiency of this method when equipped with such absorbing interface conditions. Copyright © 2006 John Wiley & Sons, Ltd. [source]


On the construction of manufactured solutions for one and two-equation eddy-viscosity models

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2007
L. Eça
Abstract This paper presents manufactured solutions (MSs) for some well-known eddy-viscosity turbulence models, viz. the Spalart & Allmaras one-equation model and the TNT and BSL versions of the two-equation k,, model. The manufactured flow solutions apply to two-dimensional, steady, wall-bounded, incompressible, turbulent flows. The two velocity components and the pressure are identical for all MSs, but various alternatives are considered for specifying the eddy-viscosity and other turbulence quantities in the turbulence models. The results obtained for the proposed MSs with a second-order accurate numerical method show that the MSs for turbulence quantities must be constructed carefully to avoid instabilities in the numerical solutions. This behaviour is model dependent: the performance of the Spalart & Allmaras and k,, models is significantly affected by the type of MS. In one of the MSs tested, even the two versions of the k,, model exhibit significant differences in the convergence properties. Copyright © 2006 John Wiley & Sons, Ltd. [source]


Block preconditioners for the discrete incompressible Navier,Stokes equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3-4 2002
Howard C. Elman
Abstract We examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady-state Navier,Stokes equations. For steady-state problems, we show that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. These characteristics are directly correlated with the convergence properties of iterative solvers, with convergence rates independent of mesh size and only mildly dependent on viscosity. For evolutionary problems, we show that implicit treatment of the time derivatives leads to systems for which convergence is essentially independent of viscosity. Copyright © 2002 John Wiley & Sons, Ltd. [source]


Least-squares parameter estimation for systems with irregularly missing data

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 7 2010
Feng Ding
Abstract This paper considers the problems of parameter identification and output estimation with possibly irregularly missing output data, using output error models. By means of an auxiliary model (or reference model) approach, we present a recursive least-squares algorithm to estimate the parameters of missing data systems, and establish convergence properties for the parameter and missing output estimation in the stochastic framework. The basic idea is to replace the unmeasurable inner variables with the output of an auxiliary model. Finally, we test the effectiveness of the algorithm with an example system. Copyright © 2009 John Wiley & Sons, Ltd. [source]


A rapidly converging filtered-error algorithm for multichannel active noise control

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 7 2007
A. 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]


Practical implementation of multichannel adaptive filters based on FTF and AP algorithms for active control

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 2-3 2005
Alberto González
Abstract In this paper, multichannel affine projection (AP) algorithms and fast transversal filters (FTF) are introduced for active noise control. A comparative practical study of the mentioned algorithms with the filtered-X LMS (F-XLMS) and the recursive least squares (RLS) is presented for multichannel systems. This study is based on simulations using real data and is mainly focused on: their computational cost and memory load, their convergence properties, their stability and their ability to create quiet zones around listener ears. Simulations show that algorithms based on FTF exhibit a good trade-off between computational cost and convergence speed. On the other hand, those based on RLS are slightly faster but they present higher computational load and stability problems in their practical implementation. It has also been observed that algorithms based on low order AP algorithms present less computational cost than the FTF-based ones but a slightly slower convergence speed. Therefore these algorithms show a desirable behaviour and versatility for practical applications. Finally, results obtained in a real-time multichannel system validate the use of AP algorithms in practical applications as an alternative to the classical multichannel F-XLMS since they provide meaningful attenuation levels, lower convergence time and similar computational cost. Additionally, as simulations indicated, AP algorithm performance can be easily improved increasing its projection order and using fast versions. Copyright © 2004 John Wiley & Sons, Ltd. [source]


Natural gradient algorithm for neural networks applied to non-linear high power amplifiers,

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 8 2002
H. Abdulkader
Abstract This paper investigates the processing techniques for non-linear high power amplifiers (HPA) using neural networks (NNs). Several applications are presented: Identification and Predistortion of the HPA. Various Neural Network structures are proposed to identify and predistort the HPA. Since a few decades, NNs have shown excellent performance in solving complex problems (like classification, recognition, etc.) but usually they suffer from slow convergence speed. Here, we propose to use the natural gradient instead of the classical ordinary gradient in order to enhance the convergence properties. Results are presented concerning identification and predistortion using classical and natural gradient. Practical implementations issues are given at the end of the paper. Copyright © 2002 John Wiley & Sons, Ltd. [source]


Integral evaluation in semiconductor device modelling using simulated annealing with Bose,Einstein statistics

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 4 2007
E.A.B. Cole
Abstract Fermi integrals arise in the mathematical and numerical modelling of microwave semiconductor devices. In particular, associated Fermi integrals involving two arguments arise in the modelling of HEMTs, in which quantum wells form at the material interfaces. The numerical evaluation of these associated integrals is time consuming. In this paper, these associated integrals are replaced by simpler functions which depend on a small number of optimal parameters. These parameters are found by optimizing a suitable cost function using a genetic algorithm with simulated annealing. A new method is introduced whereby the transition probabilities of the simulated annealing process are based on the Bose,Einstein distribution function, rather than on the more usual Maxwell,Boltzmann statistics or Tsallis statistics. Results are presented for the simulation of a four-layer HEMT, and show the effect of the approximation for the associated Fermi integrals. A comparison is made of the convergence properties of the three different statistics used in the simulated annealing process. Copyright © 2007 John Wiley & Sons, Ltd. [source]


A quasi-planar incident wave excitation for time-domain scattering analysis of periodic structures

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5 2006
David Degerfeldt
Abstract We present a quasi-planar incident wave excitation for time-domain scattering analysis of periodic structures. It uses a particular superposition of plane waves that yields an incident wave with the same periodicity as the periodic structure itself. The duration of the incident wave is controlled by means of its frequency spectrum or, equivalently, the angular spread in its constituting plane waves. Accuracy and convergence properties of the method are demonstrated by scattering computations for a planar dielectric half-space. Equipped with the proposed source, a time-domain solver based on linear elements yields an error of roughly 1% for a resolution of 20 points per wavelength and second-order convergence is achieved for smooth scatterers. Computations of the scattering characteristics for a sinusoidal surface and a random rough surface show similar performance. Copyright © 2006 John Wiley & Sons, Ltd. [source]


Finite element investigation of the ground states of the helium trimers 4He3 and 4He2,3He

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 2 2007
Moses Salci
Abstract A three-dimensional finite element method is applied to the ground states of the symmetric and asymmetric atomic helium trimers 4He3 and 4He2,3He. Three different He,He interaction potentials of hard-core nature were studied. Two extrapolation procedures based on the convergence properties of the finite element method are investigated. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source]


A comparative study on a novel model-based PID tuning and control mechanism for nonlinear systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2010
S. Iplikci
Abstract This work presents a novel predictive model-based proportional integral derivative (PID) tuning and control approach for unknown nonlinear systems. For this purpose, an NARX model of the plant to be controlled is obtained and then it used for both PID tuning and correction of the control action. In this study, for comparison, neural networks (NNs) and support vector machines (SVMs) have been used for modeling. The proposed structure has been tested on two highly nonlinear systems via simulations by comparing control and convergence performances of SVM- and NN-Based PID controllers. The simulation results have shown that when used in the proposed scheme, both NN and SVM approaches provide rapid parameter convergence and considerably high control performance by yielding very small transient- and steady-state tracking errors. Moreover, they can maintain their control performances under noisy conditions, while convergence properties are deteriorated to some extent due to the measurement noises. Copyright © 2009 John Wiley & Sons, Ltd. [source]


Pseudo alternating least squares algorithm for trilinear decomposition

JOURNAL OF CHEMOMETRICS, Issue 3 2001
Zeng-Ping Chen
Abstract In chemistry, PARAFAC is one of the most widely used algorithms for trilinear decomposition. However, the problem of PARAFAC requiring an accurate estimation of the number of factors in the system under study limits its applications to some extent. This troublesome problem has been tackled by the pseudo alternating least squares (PALS) algorithm designed in this paper. PALS is a unique algorithm which tries to alternately optimize three different objective functions to obtain the solutions for the trilinear decomposition model. It has the outstanding feature of being resistant to the influence of N (the number of factors chosen in calculation), which has been proved mathematically under some mild conditions. Although the optimization procedure of PALS is different from that of PARAFAC, an alternating least squares scheme, and hinders a straightforward analysis of its convergence properties, studies on simulated as well as real data arrays reveal that PALS can often converge to satisfactory results within a reasonable computation time, even if excess factors are used in calculation. Copyright © 2001 John Wiley & Sons, Ltd. [source]


Non-self-adjoint boundary-value problem with discontinuous density function

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2010
Murat Ad
Abstract We determine spectrum and principal functions of the non-self-adjoint differential operator corresponding to 1-D non-self-adjoint Schrödinger equation with discontinuous density function, provide some sufficient conditions guaranteeing finiteness of eigenvalues and spectral singularities, and introduce the convergence properties of principal functions. Copyright © 2009 John Wiley & Sons, Ltd. [source]


A trust-region method with a conic model for unconstrained optimization

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2008
Shao-Jian Qu
Abstract In this paper, we propose and analyze a new conic trust-region algorithm for solving the unconstrained optimization problems. A new strategy is proposed to construct the conic model and the relevant conic trust-region subproblems are solved by an approximate solution method. This approximate solution method is not only easy to implement but also preserves the strong convergence properties of the exact solution methods. Under reasonable conditions, the locally linear and superlinear convergence of the proposed algorithm is established. The numerical experiments show that this algorithm is both feasible and efficient. Copyright © 2008 John Wiley & Sons, Ltd. [source]


Electromagnetic scattering problems solved by an improved spectral iteration technique

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 6 2001
Sandra Costanzo
Abstract The spectral iteration technique is used to solve electromagnetic scattering problems. A detailed analysis is carried out to investigate the convergence properties of the procedure, and a static solution is proposed as an initial estimate of the current to solve divergence problems. Diffraction by strips is considered to validate the method. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 384,388, 2001. [source]


Characteristic-mixed covolume methods for advection-dominated diffusion problems

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 9 2006
Zhangxin Chen
Abstract Characteristic-mixed covolume methods for time-dependent advection-dominated diffusion problems are developed and studied. The diffusion term in these problems is discretized using covolume methods applied to the mixed formulation of the problems on quadrilaterals, and the temporal differentiation and advection terms are treated by characteristic tracking schemes. Three characteristic tracking schemes are studied in the context of mixed covolume methods: the modified method of characteristics, the modified method of characteristics with adjusted advection, and the Eulerian,Lagrangian localized adjoint method. The proposed methods preserve the conceptual and computational merits of both characteristics-based schemes and the mixed covolume methods. Existence and uniqueness of a solution to the discrete problem arising from the methods is shown. Stability and convergence properties of these methods are also obtained; unconditionally stable results and error estimates of optimal order are established. Copyright © 2006 John Wiley & Sons, Ltd. [source]