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Penalty Term (penalty + term)
Selected AbstractsFast iterative solution of large undrained soil-structure interaction problemsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2003Kok-Kwang Phoon Abstract In view of rapid developments in iterative solvers, it is timely to re-examine the merits of using mixed formulation for incompressible problems. This paper presents extensive numerical studies to compare the accuracy of undrained solutions resulting from the standard displacement formulation with a penalty term and the two-field mixed formulation. The standard displacement and two-field mixed formulations are solved using both direct and iterative approaches to assess if it is cost-effective to achieve more accurate solutions. Numerical studies of a simple footing problem show that the mixed formulation is able to solve the incompressible problem ,exactly', does not create pressure and stress instabilities, and obviate the need for an ad hoc penalty number. In addition, for large-scale problems where it is not possible to perform direct solutions entirely within available random access memory, it turns out that the larger system of equations from mixed formulation also can be solved much more efficiently than the smaller system of equations arising from standard formulation by using the symmetric quasi-minimal residual (SQMR) method with the generalized Jacobi (GJ) preconditioner. Iterative solution by SQMR with GJ preconditioning also is more elegant, faster, and more accurate than the popular Uzawa method. Copyright © 2003 John Wiley & Sons, Ltd. [source] Multiscale Galerkin method using interpolation wavelets for two-dimensional elliptic problems in general domainsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004Gang-Won Jang Abstract One major hurdle in developing an efficient wavelet-based numerical method is the difficulty in the treatment of general boundaries bounding two- or three-dimensional domains. The objective of this investigation is to develop an adaptive multiscale wavelet-based numerical method which can handle general boundary conditions along curved boundaries. The multiscale analysis is achieved in a multi-resolution setting by employing hat interpolation wavelets in the frame of a fictitious domain method. No penalty term or the Lagrange multiplier need to be used in the present formulation. The validity of the proposed method and the effectiveness of the multiscale adaptive scheme are demonstrated by numerical examples dealing with the Dirichlet and Neumann boundary-value problems in quadrilateral and quarter circular domains. Copyright © 2003 John Wiley & Sons, Ltd. [source] The effect of a penalty term involving higher order derivatives on the distribution of phases in an elastic medium with a two-well elastic potentialMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2002M. Bildhauer Abstract We consider the problem of minimizing 0 Incorporating a class of constraints into the dynamics of optimal control problemsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 6 2009K. Graichen Abstract A method is proposed to systematically transform a constrained optimal control problem (OCP) into an unconstrained OCP, which can be treated in the standard calculus of variations. The considered class of constraints comprises up to m input constraints and m state constraints with well-defined relative degree, where m denotes the number of inputs of the given nonlinear system. Starting from an equivalent normal form representation, the constraints are incorporated into a new system dynamics by means of saturation functions and differentiation along the normal form cascade. This procedure leads to a new unconstrained OCP, where an additional penalty term is introduced to avoid the unboundedness of the saturation function arguments if the original constraints are touched. The penalty parameter has to be successively reduced to converge to the original optimal solution. The approach is independent of the method used to solve the new unconstrained OCP. In particular, the constraints cannot be violated during the numerical solution and a successive reduction of the constraints is possible, e.g. to start from an unconstrained solution. Two examples in the single and multiple input case illustrate the potential of the approach. For these examples, a collocation method is used to solve the boundary value problems stemming from the optimality conditions. Copyright © 2009 John Wiley & Sons, Ltd. [source] A note on penalized minimum distance estimation in nonparametric regressionTHE CANADIAN JOURNAL OF STATISTICS, Issue 3 2003Florentina Bunea Abstract The authors introduce a penalized minimum distance regression estimator. They show the estimator to balance, among a sequence of nested models of increasing complexity, the L1 -approximation error of each model class and a penalty term which reflects the richness of each model and serves as a upper bound for the estimation error. Les auteurs présentent un nouvel estimateur de régression obtenu par minimisation d'une distance pénalisée. Ils montrent que pour une suite de modèles embo,tés à complexité croissante, cet estimateur offre un bon compromis entre l'erreur d'approximation L1 de chaque classe de modèles et un terme de pénalisation permettant à la fois de refléter la richesse de chaque modèle et de majorer l'erreur d'estimation. [source] Akaike's Information Criterion in Generalized Estimating EquationsBIOMETRICS, Issue 1 2001Wei Pan Summary. Correlated response data are common in biomedical studies. Regression analysis based on the generalized estimating equations (GEE) is an increasingly important method for such data. However, there seem to be few model-selection criteria available in GEE. The well-known Akaike Information Criterion (AIC) cannot be directly applied since AIC is based on maximum likelihood estimation while GEE is nonlikelihood based. We propose a modification to AIC, where the likelihood is replaced by the quasi-likelihood and a proper adjustment is made for the penalty term. Its performance is investigated through simulation studies. For illustration, the method is applied to a real data set. [source] A hybrid discontinuous Galerkin/interface method for the computational modelling of failureINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2004J. Mergheim Abstract The present contribution is concerned with the computational modelling of failure along well-defined surfaces, which occur for example in the case of light-weight composite materials. A hybrid method will be introduced which makes use of the discontinuous Galerkin method in combination with a finite element interface approach. As a natural choice interface elements are introduced along the known failure surface. The discontinuous Galerkin method is applied in the pre-failure regime to avoid the unphysical use of penalty terms and instead to enforce the continuity of the solution along the interface weakly. Once a particular failure criterion is fulfilled, the behaviour of the interface is determined constitutively, depending on the displacement jump. The applicability of the proposed method is illustrated by means of two computational model problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] A relaxed model and its homogenization for nematic liquid crystals in composite materialsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2004Quan Shen Abstract We analyse a model for equilibrium configurations of composite systems of nematic liquid crystal with polymer inclusions, in the presence of an external magnetic field. We assume that the system has a periodic structure, and consider the relaxed problem on the unit length constraint of the nematic director field. The relaxation of the Oseen,Frank energy functional is carried out by including bulk as well as surface energy penalty terms, rendering the problem fully non-linear. We employ two-scale convergence methods to obtain effective configurations of the system, as the size of the polymeric inclusions tends to zero. We discuss the minimizers of the effective energies for, both, the constrained as well as the unconstrained models. Copyright © 2004 John Wiley & Sons, Ltd. [source] Variable Selection for Model-Based High-Dimensional Clustering and Its Application to Microarray DataBIOMETRICS, Issue 2 2008Sijian Wang Summary Variable selection in high-dimensional clustering analysis is an important yet challenging problem. In this article, we propose two methods that simultaneously separate data points into similar clusters and select informative variables that contribute to the clustering. Our methods are in the framework of penalized model-based clustering. Unlike the classical L1 -norm penalization, the penalty terms that we propose make use of the fact that parameters belonging to one variable should be treated as a natural "group." Numerical results indicate that the two new methods tend to remove noninformative variables more effectively and provide better clustering results than the L1 -norm approach. [source]
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