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Convergence Results (convergence + result)
Selected AbstractsConvergence of coercive approximations for a model of gradient type in poroplasticityMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2009Sebastian Owczarek Abstract We study the existence theory to the quasi-static initial-boundary-value problem of poroplasticity. In this article the classical quasi-static Biot model is considered for soil consolidation coupled with a nonlinear system of differential equations. This work, for the poroplasticity model of monotone-gradient type, presents a convergence result of the coercive approximation to the solution of the original noncoercive problem. Copyright © 2008 John Wiley & Sons, Ltd. [source] Some preconditioners for the CFIE equation of electromagnetismMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2008David P. Levadoux Abstract We present three weak parametrices of the operator of the combined field integral equation (CFIE). An interesting feature of these parametrices is that they are compatible with different discretization strategies and hence allow for the construction of efficient preconditioners dedicated to the CFIE. Their numerical analysis shows that a regularization process acting at the continuous level of the equation is also effective at the discrete level if the mesh size tends to zero. First numerical tests confirm this effect and preconditioning is observed indeed. Furthermore, we show that the underlying operator of CFIE satisfies a uniform discrete Inf,Sup condition that allows one to predict an original convergence result for the numerical solution of CFIE to the exact one. Copyright © 2008 John Wiley & Sons, Ltd. [source] Homogenizing the acoustic properties of a porous matrix containing an incompressible inviscid fluidMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2003J. L. Ferrin We undertake a rigorous derivation of the Biot's law for a porous elastic solid containing an inviscid fluid. We consider small displacements of a linear elastic solid being itself a connected periodic skeleton containing a pore structure of the characteristic size ,. It is completely saturated by an incompressible inviscid fluid. The model is described by the equations of the linear elasticity coupled with the linearized incompressible Euler system. We study the homogenization limit when the pore size ,tends to zero. The main difficulty is obtaining an a priori estimate for the gradient of the fluid velocity in the pore structure. Under the assumption that the solid part is connected and using results on the first order elliptic systems, we obtain the required estimate. It allows us to apply appropriate results from the 2-scale convergence. Then it is proved that the microscopic displacements and the fluid pressure converge in 2-scales towards a linear hyperbolic system for an effective displacement and an effective pressure field. Using correctors, we also give a strong convergence result. The obtained system is then compared with the Biot's law. It is found that there is a constitutive relation linking the effective pressure with the divergences of the effective fluid and solid displacements. Then we prove that the homogenized model coincides with the Biot's equations but with the added mass ,a being a matrix, which is calculated through an auxiliary problem in the periodic cell for the tortuosity. Furthermore, we get formulas for the matricial coefficients in the Biot's effective stress,strain relations. Finally, we consider the degenerate case when the fluid part is not connected and obtain Biot's model with the relative fluid displacement equal to zero. Copyright © 2003 John Wiley & Sons, Ltd. [source] Some observations on the l2 convergence of the additive Schwarz preconditioned GMRES methodNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 5 2002Xiao-Chuan Cai Abstract Additive Schwarz preconditioned GMRES is a powerful method for solving large sparse linear systems of equations on parallel computers. The algorithm is often implemented in the Euclidean norm, or the discrete l2 norm, however, the optimal convergence result is available only in the energy norm (or the equivalent Sobolev H1 norm). Very little progress has been made in the theoretical understanding of the l2 behaviour of this very successful algorithm. To add to the difficulty in developing a full l2 theory, in this note, we construct explicit examples and show that the optimal convergence of additive Schwarz preconditioned GMRES in l2 cannot be obtained using the existing GMRES theory. More precisely speaking, we show that the symmetric part of the preconditioned matrix, which plays a role in the Eisenstat,Elman,Schultz theory, has at least one negative eigenvalue, and we show that the condition number of the best possible eigenmatrix that diagonalizes the preconditioned matrix, key to the Saad,Schultz theory, is bounded from both above and below by constants multiplied by h,1/2. Here h is the finite element mesh size. The results presented in this paper are mostly negative, but we believe that the techniques used in our proofs may have wide applications in the further development of the l2 convergence theory and in other areas of domain decomposition methods. Copyright © 2002 John Wiley & Sons, Ltd. [source] Nonparametric two-step regression estimation when regressors and error are dependentTHE CANADIAN JOURNAL OF STATISTICS, Issue 2 2000Jons Pinkse Abstract This paper considers estimation of the function g in the model Yt = g(Xt ) + ,t when E(,t|Xt) , 0 with nonzero probability. We assume the existence of an instrumental variable Zt that is independent of ,t, and of an innovation ,t = Xt , E(Xt|Zt). We use a nonparametric regression of Xt on Zt to obtain residuals ,t, which in turn are used to obtain a consistent estimator of g. The estimator was first analyzed by Newey, Powell & Vella (1999) under the assumption that the observations are independent and identically distributed. Here we derive a sample mean-squared-error convergence result for independent identically distributed observations as well as a uniform-convergence result under time-series dependence. Cet article concerne l'estimation de la fonction g dans le modèle Yt = g(Xt) + ,t où E(,t| Xt) , 0 avec probabilité non nulle. Les auteurs supposent l'existence d'une 'variable instrumentale' Zt qui est indépendante de ,t et de l'innovation ,t = Xt , E(Xt|Zt). Les résidus ,t déduits d'une régression non paramétrique de Xt sur Zt permettent d'obtenir une estimation convergente de g. Cette façon de procéder avait déjà été proposée par Newey, Powell & Vella (1999) dans le cas où les observations for-ment un échantillon aléatoire. Les auteurs démontrent ici la convergence de 1'erreur quadratique moyenne expérimentale sous les m,mes conditions et établissent un résultat de convergence uniforme sous des conditions de dépendance sérielle entre les observations. [source] Consistent tangent matrices for density-dependent finite plasticity modelsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2001Agustí Pérez-Foguet Abstract The consistent tangent matrix for density-dependent plastic models within the theory of isotropic multiplicative hyperelastoplasticity is presented here. Plastic equations expressed as general functions of the Kirchhoff stresses and density are considered. They include the Cauchy-based plastic models as a particular case. The standard exponential return-mapping algorithm is applied, with the density playing the role of a fixed parameter during the nonlinear plastic corrector problem. The consistent tangent matrix has the same structure as in the usual density-independent plastic models. A simple additional term takes into account the influence of the density on the plastic corrector problem. Quadratic convergence results are shown for several representative examples involving geomaterial and powder constitutive models. Copyright © 2001 John Wiley & Sons, Ltd. [source] Comparative study of the least squares approximation of the modified Bessel functionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2008Jianguo XinArticle first published online: 14 DEC 200 Abstract The least squares problem of the modified Bessel function of the second kind has been considered in this study with the Fourier series, Tchebycheff and Legendre approximation. Numerical evidence shows that the Gibbs phenomenon exists in the approximation with the truncated Fourier series, thus, giving poor convergence results compared with the other polynomial bases. For the latter two cases, the Legendre series perform better than Tchebycheff series in terms of the ,2 norm of the relative errors for each order of the polynomial approximation, and the ratio of the ,2 norm of the relative errors from the corresponding approximation seems to be a constant value of 1.3. Copyright © 2006 John Wiley & Sons, Ltd. [source] A genetic-based neuro-fuzzy controller for blind equalization of time-varying channelsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 7 2008Siba Prasada Panigrahi Abstract This paper presents a neuro-fuzzy network (NFN) where all its parameters can be tuned simultaneously using genetic algorithms (GAs). The approach combines the merits of fuzzy logic theory, neural networks and GAs. The proposed NFN does not require a priori knowledge about the system and eliminates the need for complicated design steps such as manual tuning of input,output membership functions, and selection of fuzzy rule base. Although, only conventional GAs have been used, convergence results are very encouraging. A well-known numerical example derived from literature is used to evaluate and compare the performance of the network with other equalizing approaches. Simulation results show that the proposed neuro-fuzzy controller, all parameters of which have been tuned simultaneously using GAs, offers advantages over existing equalizers and has improved performance. From the perspective of application and implementation, this paper is very interesting as it provides a new method for performing blind equalization. The main contribution of this paper is the use of learning algorithms to train a feed-forward neural network for M-ary QAM and PSK signals. This paper also provides a platform for researchers of the area for further development. Copyright © 2008 John Wiley & Sons, Ltd. [source] Is the convergence of business cycles a global or regional issue?INTERNATIONAL JOURNAL OF FINANCE & ECONOMICS, Issue 3 2006Euroland, The UK Abstract The identification of an European business cycle has been inconclusive. Yet cyclical convergence is the key consideration for those countries that wish to be members of the currency union (e.g. UK). In general, countries will vary in the components and characteristics that make up their cycles at any moment, as well as in the state of their cycle at each moment. To take this into account, we show here how to decompose a business cycle in a time-frequency framework; so that its components vary in importance and cyclical characteristics over time. We show, the inconclusive convergence results obtained so far appear because countries have some cycles in common,but diverge at others. Copyright © 2006 John Wiley & Sons, Ltd. [source] Performance of algebraic multigrid methods for non-symmetric matrices arising in particle methodsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2-3 2010B. Seibold Abstract Large linear systems with sparse, non-symmetric matrices are known to arise in the modeling of Markov chains or in the discretization of convection,diffusion problems. Due to their potential of solving sparse linear systems with an effort that is linear in the number of unknowns, algebraic multigrid (AMG) methods are of fundamental interest for such systems. For symmetric positive definite matrices, fundamental theoretical convergence results are established, and efficient AMG solvers have been developed. In contrast, for non-symmetric matrices, theoretical convergence results have been provided only recently. A property that is sufficient for convergence is that the matrix be an M-matrix. In this paper, we present how the simulation of incompressible fluid flows with particle methods leads to large linear systems with sparse, non-symmetric matrices. In each time step, the Poisson equation is approximated by meshfree finite differences. While traditional least squares approaches do not guarantee an M-matrix structure, an approach based on linear optimization yields optimally sparse M-matrices. For both types of discretization approaches, we investigate the performance of a classical AMG method, as well as an algebraic multilevel iteration (AMLI) type method. While in the considered test problems, the M-matrix structure turns out not to be necessary for the convergence of AMG, problems can occur when it is violated. In addition, the matrices obtained by the linear optimization approach result in fast solution times due to their optimal sparsity. Copyright © 2010 John Wiley & Sons, Ltd. [source] Do family farms really converge to a uniform size?AUSTRALIAN JOURNAL OF AGRICULTURAL & RESOURCE ECONOMICS, Issue 1 2010The role of unobserved farm efficiency We analyse the growth of family farms in Israeli cooperative villages during a period of economic turmoil. We use instrumental variables to account for the endogeneity of initial farm size, and correct for selectivity as a result of farm survival. We also include a technical efficiency index, derived from the estimation of a stochastic frontier production model, as an explanatory variable. Our aim is to check whether ignoring efficiency could have been the reason for convergence results obtained elsewhere in the literature. We found that technical efficiency is an important determinant of farm growth, and that not controlling for technical efficiency could seriously bias the results. In particular, larger farms are found to grow faster over time, while without controlling for technical efficiency the farm growth process seemed to be independent of initial farm size. The increasing polarisation of farm sizes in Israel has ramifications for the inefficiencies induced by the historical quota system, for the political power of the farm sector and for the social stability of farm communities. [source] | ||||||||||||||||