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Lagrange Multipliers (lagrange + multiplier)
Terms modified by Lagrange Multipliers Selected AbstractsGeneralized Method of Moments With Many Weak Moment ConditionsECONOMETRICA, Issue 3 2009Whitney K. Newey Using many moment conditions can improve efficiency but makes the usual generalized method of moments (GMM) inferences inaccurate. Two-step GMM is biased. Generalized empirical likelihood (GEL) has smaller bias, but the usual standard errors are too small in instrumental variable settings. In this paper we give a new variance estimator for GEL that addresses this problem. It is consistent under the usual asymptotics and, under many weak moment asymptotics, is larger than usual and is consistent. We also show that the Kleibergen (2005) Lagrange multiplier and conditional likelihood ratio statistics are valid under many weak moments. In addition, we introduce a jackknife GMM estimator, but find that GEL is asymptotically more efficient under many weak moments. In Monte Carlo examples we find that t -statistics based on the new variance estimator have nearly correct size in a wide range of cases. [source] Application of second-order adjoint technique for conduit flow problemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2007T. Kurahashi Abstract This paper presents the way to obtain the Newton gradient by using a traction given by the perturbation for the Lagrange multiplier. Conventionally, the second-order adjoint model using the Hessian/vector products expressed by the product of the Hessian matrix and the perturbation of the design variables has been researched (Comput. Optim. Appl. 1995; 4:241,262). However, in case that the boundary value would like to be obtained, this model cannot be applied directly. Therefore, the conventional second-order adjoint technique is extended to the boundary value determination problem and the second-order adjoint technique is applied to the conduit flow problem in this paper. As the minimization technique, the Newton-based method is employed. The Broyden,Fletcher,Goldfarb,Shanno (BFGS) method is applied to calculate the Hessian matrix which is used in the Newton-based method and a traction given by the perturbation for the Lagrange multiplier is used in the BFGS method. Copyright © 2007 John Wiley & Sons, Ltd. [source] Evaluating Specification Tests for Markov-Switching Time-Series ModelsJOURNAL OF TIME SERIES ANALYSIS, Issue 4 2008Daniel R. Smith C12; C15; C22 Abstract., We evaluate the performance of several specification tests for Markov regime-switching time-series models. We consider the Lagrange multiplier (LM) and dynamic specification tests of Hamilton (1996) and Ljung,Box tests based on both the generalized residual and a standard-normal residual constructed using the Rosenblatt transformation. The size and power of the tests are studied using Monte Carlo experiments. We find that the LM tests have the best size and power properties. The Ljung,Box tests exhibit slight size distortions, though tests based on the Rosenblatt transformation perform better than the generalized residual-based tests. The tests exhibit impressive power to detect both autocorrelation and autoregressive conditional heteroscedasticity (ARCH). The tests are illustrated with a Markov-switching generalized ARCH (GARCH) model fitted to the US dollar,British pound exchange rate, with the finding that both autocorrelation and GARCH effects are needed to adequately fit the data. [source] New Improved Tests for Cointegration with Structural BreaksJOURNAL OF TIME SERIES ANALYSIS, Issue 2 2007Joakim Westerlund C12; C32; C33 Abstract., This article proposes Lagrange multiplier-based tests for the null hypothesis of no cointegration. The tests are general enough to allow for heteroskedastic and serially correlated errors, deterministic trends, and a structural break of unknown timing in both the intercept and slope. The limiting distributions of the test statistics are derived, and are found to be invariant not only with respect to the trend and structural break, but also with respect to the regressors. A small Monte Carlo study is also conducted to investigate the small-sample properties of the tests. The results reveal that the tests have small size distortions and good power relative to other tests. [source] Simultaneous solution of Lagrangean dual problems interleaved with preprocessing for the weight constrained shortest path problemNETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2009Ranga Muhandiramge Abstract Conventional Lagrangean preprocessing for the network Weight Constrained Shortest Path Problem (WCSPP), for example Beasley and Christofides (Beasley and Christofides, Networks 19 (1989), 379,394), calculates lower bounds on the cost of using each node and edge in a feasible path using a single optimal Lagrange multiplier for the relaxation of the WCSPP. These lower bounds are used in conjunction with an upper bound to eliminate nodes and edges. However, for each node and edge, a Lagrangean dual problem exists whose solution may differ from the relaxation of the full problem. Thus, using one Lagrange multiplier does not offer the best possible network reduction. Furthermore, eliminating nodes and edges from the network may change the Lagrangean dual solutions in the remaining reduced network, warranting an iterative solution and reduction procedure. We develop a method for solving the related Lagrangean dual problems for each edge simultaneously which is iterated with eliminating nodes and edges. We demonstrate the effectiveness of our method computationally: we test it against several others and show that it both reduces solve time and the number of intractable problems encountered. We use a modified version of Carlyle and Wood's (38th Annual ORSNZ Conference, Hamilton, New Zealand, November, 2003) enumeration algorithm in the gap closing stage. We also make improvements to this algorithm and test them computationally. © 2009 Wiley Periodicals, Inc. NETWORKS, 2009 [source] On the mixed finite element method with Lagrange multipliersNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2003Ivo Babu Abstract In this note we analyze a modified mixed finite element method for second-order elliptic equations in divergence form. As a model we consider the Poisson problem with mixed boundary conditions in a polygonal domain of R2. The Neumann (essential) condition is imposed here in a weak sense, which yields the introduction of a Lagrange multiplier given by the trace of the solution on the corresponding boundary. This approach allows to handle nonhomogeneous Neumann boundary conditions, theoretically and computationally, in an alternative and usually easier way. Then we utilize the classical Babu,ka-Brezzi theory to show that the resulting mixed variational formulation is well posed. In addition, we use Raviart-Thomas spaces to define the associated finite element method and, applying some elliptic regularity results, we prove the stability, unique solvability, and convergence of this discrete scheme, under appropriate assumptions on the mesh sizes. Finally, we provide numerical results illustrating the performance of the algorithm for smooth and singular problems. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 192,210, 2003 [source] Refined mixed finite element method for the elasticity problem in a polygonal domainNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2002M. Farhloul Abstract The purpose of this article is to study a mixed formulation of the elasticity problem in plane polygonal domains and its numerical approximation. In this mixed formulation the strain tensor is introduced as a new unknown and its symmetry is relaxed by a Lagrange multiplier, which is nothing else than the rotation. Because of the corner points, the displacement field is not regular in general in the vicinity of the vertices but belongs to some weighted Sobolev space. Using this information, appropriate refinement rules are imposed on the family of triangulations in order to recapture optimal error estimates. Moreover, uniform error estimates in the Lamé coefficient , are obtained for , large. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 323,339, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10009 [source] Testing for stationarity in heterogeneous panel dataTHE ECONOMETRICS JOURNAL, Issue 2 2000Kaddour Hadri This paper proposes a residual-based Lagrange multiplier (LM) test for a null that the individual observed series are stationary around a deterministic level or around a deterministic trend against the alternative of a unit root in panel data. The tests which are asymptotically similar under the null, belong to the locally best invariant (LBI) test statistics. The asymptotic distributions of the statistics are derived under the null and are shown to be normally distributed. Finite sample sizes and powers are considered in a Monte Carlo experiment. The empirical sizes of the tests are close to the true size even in small samples. The testing procedure is easy to apply, including, to panel data models with fixed effects, individual deterministic trends and heterogeneous errors across cross-sections. It is also shown how to apply the tests to the more general case of serially correlated disturbance terms. [source] On the Quantile Regression Based Tests for Asymmetry in Stock Return VolatilityASIAN ECONOMIC JOURNAL, Issue 2 2002Beum-Jo Park This paper attempts to examine whether the asymmetry of stock return volatility varies with the level of volatility. Thus, quantile regression based tests (,-tests) are presupposed. These tests differ from the diagnostic tests introduced by Engle and Ng (1993) insofar as they can provide a complete picture of asymmetries in volatility across quantiles of variance distribution and, in case of non-normal errors, they have improved power due to their robustness against non-normality. A small Monte Carlo evidence suggests that the Wald and likelihood ratio (LR) tests out of ,-tests are reasonable, showing that they outperform the Lagrange multiplier (LM) test based on least squares residuals when the innovations exhibit heavy tail. Using the normalized residuals obtained from AR(1)-GARCH(1, 1) estimation, the test results demonstrated that only the TOPIX out of six stock-return series had asymmetry in volatility at moderate level, while all stock return series except the FAZ and FA100 had more significant asymmetry in volatility at higher levels. Interestingly, it is clear from the empirical findings that, like hypothesis of leverage effects, volatility of the TOPIX, CAC40, and, MIB tends to respond significantly to extremely negative shock at high level, but is not correlated with any positive shock. These might be valuable findings that have not been seriously considered in past research, which has focussed only on mean level of volatility. [source] Force/motion sliding mode control of three typical mechanismsASIAN JOURNAL OF CONTROL, Issue 2 2009Rong-Fong Fung Abstract This paper proposes a sliding mode control (SMC) algorithm for trajectory tracking of the slider-crank mechanism, quick-return mechanism, and toggle mechanism. First, the dynamic models suitable for the controls of both the motion and constrained force are derived using Hamilton's principle, the Lagrange multiplier, and implicit function theory. Second, the SMC is designed to ensure the input torques can achieve trajectory tracking on the constrained surfaces with specific constraint forces. Finally, the developed method is successfully verified for effectiveness of the force/motion controls for these three typical mechanisms from the results of simulation. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Impulse-based dynamic simulation in linear timeCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 4-5 2007Jan Bender Abstract This paper describes an impulse-based dynamic simulation method for articulated bodies which has a linear time complexity. Existing linear-time methods are either based on a reduced-coordinate formulation or on Lagrange multipliers. The impulse-based simulation has advantages over these well-known methods. Unlike reduced-coordinate methods, it handles nonholonomic constraints like velocity-dependent ones and is very easy to implement. In contrast to Lagrange multiplier methods the impulse-based approach has no drift problem and an additional stabilisation is not necessary. The presented method computes a simulation step in O(n) time for acyclic multi-body systems containing equality constraints. Closed kinematic chains can be handled by dividing the model into different acyclic parts. Each of these parts is solved independently from each other. The dependencies between the single parts are solved by an iterative method. In the same way inequality constraints can be integrated in the simulation process in order to handle collisions and permanent contacts with dynamic and static friction. Copyright © 2007 John Wiley & Sons, Ltd. [source] Analyzing Bank Filtration by Deconvoluting Time Series of Electric ConductivityGROUND WATER, Issue 3 2007Olaf A. Cirpka Knowing the travel-time distributions from infiltrating rivers to pumping wells is important in the management of alluvial aquifers. Commonly, travel-time distributions are determined by releasing a tracer pulse into the river and measuring the breakthrough curve in the wells. As an alternative, one may measure signals of a time-varying natural tracer in the river and in adjacent wells and infer the travel-time distributions by deconvolution. Traditionally this is done by fitting a parametric function such as the solution of the one-dimensional advection-dispersion equation to the data. By choosing a certain parameterization, it is impossible to determine features of the travel-time distribution that do not follow the general shape of the parameterization, i.e., multiple peaks. We present a method to determine travel-time distributions by nonparametric deconvolution of electric-conductivity time series. Smoothness of the inferred transfer function is achieved by a geostatistical approach, in which the transfer function is assumed as a second-order intrinsic random time variable. Nonnegativity is enforced by the method of Lagrange multipliers. We present an approach to directly compute the best nonnegative estimate and to generate sets of plausible solutions. We show how the smoothness of the transfer function can be estimated from the data. The approach is applied to electric-conductivity measurements taken at River Thur, Switzerland, and five wells in the adjacent aquifer, but the method can also be applied to other time-varying natural tracers such as temperature. At our field site, electric-conductivity fluctuations appear to be an excellent natural tracer. [source] Study on the action of the active earth pressure by variational limit equilibrium methodINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2010Li Xinggao Abstract Within the framework of limiting equilibrium approach, the problem of active earth pressure on rigid retaining wall is formulated in terms of the calculus of variations by means of Lagrange multipliers. It is transcribed as the functional of extreme-value problem by two undetermined function arguments, and is further transformed into determining the minimax solution of restrained functions incorporating the geometrical relations of the problem. The function of (fmincon) in the optimization toolbox of MATLAB 6.1 can be used to find the minimax solution. Computation results show there exist two kinds of modes of failure sliding along plane surface and rotating around log-spiral cylinder surface when the soil behind the walls reaches the critical active state. The magnitude of active earth pressure in the case of translational mode is less than that in the case of rotational mode. The location of action point of earth pressure in the case of translational mode is at or below height of the wall, and in the case of rotational mode, is above height of the wall. Preliminary study indicates a pair of numbers by two theoretical modes can be regarded as an interval estimation of active pressure. Copyright © 2009 John Wiley & Sons, Ltd. [source] Analysis of adiabatic shear bands in heat-conducting elastothermoviscoplastic materials by the meshless local Bubnov,Galerkin methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2009R. C. Batra Abstract Transient finite coupled thermomechanical simple shearing deformations of a block made of an elastothermoviscoplastic material that exhibits strain and strain-rate hardening, and thermal softening are studied by using the meshless local Bubnov,Galerkin method. A local nonlinear weak formulation and a semidiscrete formulation of the problem are derived. The prescribed velocity at the top and the bottom surfaces of the block is enforced by using a set of Lagrange multipliers. A homogeneous solution of the problem is perturbed by superimposing on it a temperature bump at the center of the block, and the resulting nonlinear initial-boundary-value problem is solved numerically. We have developed an integration scheme to numerically integrate the set of coupled nonlinear ordinary differential equations. The inhomogeneous deformations of the block are found to concentrate in a narrow region of intense plastic deformation usually called a shear band. For a material exhibiting enhanced thermal softening, it is shown that as the shear stress within the region of localization collapses, an unloading elastic shear wave emanates outward from the edges of the shear band. In the absence of an analytical solution, the computed results have been compared with those obtained by the finite element and the modified smoothed particle hydrodynamics methods. Copyright © 2008 John Wiley & Sons, Ltd. [source] Coupling of mesh-free methods with finite elements: basic concepts and test resultsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2006T. Rabczuk Abstract This paper reviews several novel and older methods for coupling mesh-free particle methods, particularly the element-free Galerkin (EFG) method and the smooth particle hydrodynamics (SPH), with finite elements (FEs). We study master,slave couplings where particles are fixed across the FE boundary, coupling via interface shape functions such that consistency conditions are satisfied, bridging domain coupling, compatibility coupling with Lagrange multipliers and hybrid coupling methods where forces from the particles are applied via their shape functions on the FE nodes and vice versa. The hybrid coupling methods are well suited for large deformations and adaptivity and the coupling procedure is independent of the particle distance and nodal arrangement. We will study the methods for several static and dynamic applications, compare the results to analytical and experimental data and show advantages and drawbacks of the methods. Copyright © 2006 John Wiley & Sons, Ltd. [source] Simulation of special loading conditions by means of non-linear constraints imposed through Lagrange multipliersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2002M. A. Gutiérrez Abstract This paper discusses the necessity and handling of non-linear constraint equations to describe the behaviour of properties of the loading system such as, e.g. smooth free-rotating loading platens. An exact, non-linear formulation for a smooth loading platen is derived and its incorporation into the equilibrium equations is presented. For this purpose, the Lagrange multiplier method is used. The solution of the equilibrium equations by means of a Newton,Raphson algorithm is also outlined. The proposed approach is validated on a patch of two finite elements and applied to a compression-bending test on a pre-notched specimen. It is observed that use of a linearized approximation of the boundary constraint can lead to errors in the description of the motion of the constrained nodes. Thus, the non-linear formulation is preferable. Copyright © 2002 John Wiley & Sons, Ltd. [source] Imposition of essential boundary conditions by displacement constraint equations in meshless methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2001Xiong Zhang Abstract One of major difficulties in the implementation of meshless methods is the imposition of essential boundary conditions as the approximations do not pass through the nodal parameter values. As a consequence, the imposition of essential boundary conditions in meshless methods is quite awkward. In this paper, a displacement constraint equations method (DCEM) is proposed for the imposition of the essential boundary conditions, in which the essential boundary conditions is treated as a constraint to the discrete equations obtained from the Galerkin methods. Instead of using the methods of Lagrange multipliers and the penalty method, a procedure is proposed in which unknowns are partitioned into two subvectors, one consisting of unknowns on boundary ,u, and one consisting of the remaining unknowns. A simplified displacement constraint equations method (SDCEM) is also proposed, which results in a efficient scheme with sufficient accuracy for the imposition of the essential boundary conditions in meshless methods. The present method results in a symmetric, positive and banded stiffness matrix. Numerical results show that the accuracy of the present method is higher than that of the modified variational principles. The present method is a exact method for imposing essential boundary conditions in meshless methods, and can be used in Galerkin-based meshless method, such as element-free Galerkin methods, reproducing kernel particle method, meshless local Petrov,Galerkin method. Copyright © 2001 John Wiley & Sons, Ltd. [source] A discontinuous enrichment method for the efficient solution of plate vibration problems in the medium-frequency regimeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2010Paolo Massimi Abstract A discontinuous enrichment method (DEM) is presented for the efficient discretization of plate vibration problems in the medium-frequency regime. This method enriches the polynomial shape functions of the classical finite element discretization with free-space solutions of the biharmonic operator governing the elastic vibrations of an infinite Kirchhoff plate. These free-space solutions, which represent flexural waves and decaying modes, are discontinuous across the element interfaces. For this reason, two different and carefully constructed Lagrange multiplier approximations are introduced along the element edges to enforce a weak continuity of the transversal displacement and its normal derivative, and discrete Lagrange multipliers are introduced at the element corners to enforce there a weak continuity of the transversal displacement. The proposed DEM is illustrated with the solution of sample plate vibration problems with different types of harmonic loading in the medium-frequency regime, away from and close to resonance. In all cases, its performance is found to be significantly superior to that of the classical higher-order finite element method. Copyright © 2010 John Wiley & Sons, Ltd. [source] Multi-time-step domain coupling method with energy controlINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010N. Mahjoubi Abstract A multi-time-step integration method is proposed for solving structural dynamics problems on multiple domains. The method generalizes earlier state-space integration algorithms by introducing displacement constraints via Lagrange multipliers, representing the time-integrated constraint forces over the individual time step. It is demonstrated that displacement continuity between the subdomains leads to cancelation of the interface contributions to the energy balance equation, and thus stability and algorithmic damping properties of the original algorithms are retained. The various subdomains can be integrated in time using different time steps and/or different state-space time integration schemes. The solution of the constrained system equations is obtained using a dual Schur formulation, allowing for maximum independence of the calculation of the subdomains. Stability and accuracy are illustrated by a numerical example using a refined mesh around concentrated forces. Copyright © 2010 John Wiley & Sons, Ltd. [source] A dual mortar approach for 3D finite deformation contact with consistent linearizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010Alexander Popp Abstract In this paper, an approach for three-dimensional frictionless contact based on a dual mortar formulation and using a primal,dual active set strategy for direct constraint enforcement is presented. We focus on linear shape functions, but briefly address higher order interpolation as well. The study builds on previous work by the authors for two-dimensional problems. First and foremost, the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi-smooth Newton method are extended to the 3D case. This allows for solving all types of nonlinearities (i.e. geometrical, material and contact) within one single Newton scheme. Owing to the dual Lagrange multiplier approach employed, this advantage is not accompanied by an undesirable increase in system size as the Lagrange multipliers can be condensed from the global system of equations. Moreover, it is pointed out that the presented method does not make use of any regularization of contact constraints. Numerical examples illustrate the efficiency of our method and the high quality of results in 3D finite deformation contact analysis. Copyright © 2010 John Wiley & Sons, Ltd. [source] A continuum-to-atomistic bridging domain method for composite latticesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Mei Xu Abstract The bridging domain method is an overlapping domain decomposition approach for coupling finite element continuum models and molecular mechanics models. In this method, the total energy is decomposed into atomistic and continuum parts by complementary weight functions applied to each part of the energy in the coupling domain. To enforce compatibility, the motions of the coupled atoms are constrained by the continuum displacement field using Lagrange multipliers. For composite lattices, this approach is suboptimal because the internal modes of the lattice are suppressed by the homogeneous continuum displacement field in the coupling region. To overcome this difficulty, we present a relaxed bridging domain method. In this method, the atom set is divided into primary and secondary atoms; the relative motions between them are often called the internal modes. Only the primary atoms are constrained in the coupling region, which succeed in allowing these internal modes to fully relax. Several one- and two-dimensional examples are presented, which demonstrate improved accuracy over the standard bridging domain method. Copyright © 2009 John Wiley & Sons, Ltd. [source] A space,time discontinuous Galerkin method for the solution of the wave equation in the time domainINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2009Steffen Petersen Abstract In recent years, the focus of research in the field of computational acoustics has shifted to the medium frequency regime and multiscale wave propagation. This has led to the development of new concepts including the discontinuous enrichment method. Its basic principle is the incorporation of features of the governing partial differential equation in the approximation. In this contribution, this concept is adapted for the simulation of transient problems governed by the wave equation. We present a space,time discontinuous Galerkin method with Lagrange multipliers, where the shape approximation in space and time is based on solutions of the homogeneous wave equation. The use of hierarchical wave-like basis functions is enabled by means of a variational formulation that allows for discontinuities in both the spatial and the temporal discretizations. Numerical examples in one space dimension demonstrate the outstanding performance of the proposed method compared with conventional space,time finite element methods. Copyright © 2008 John Wiley & Sons, Ltd. [source] Bridging domain methods for coupled atomistic,continuum models with L2 or H1 couplingsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2009P.-A. Guidault Abstract A bridging domain method for coupled atomistic,continuum models is proposed that enables to compare various coupling terms. The approach does not require the finite element mesh to match the lattice spacing of the atomic model. It is based on an overlapping domain decomposition method that makes use of Lagrange multipliers and weight functions in the coupling zone in order to distribute the energy between the two competing models. Two couplings are investigated. The L2 coupling enforces the continuity of displacements between the two models directly. The H1 coupling involves the definition of a strain measure. For this purpose, a moving least-square interpolant of the atomic displacement is defined. The choice of the weight functions is studied. Patch tests and a graphene sheet with a crack are studied. It is shown that both continuous and discontinuous weight functions can be used with the H1 coupling whereas the L2 coupling requires continuous weight functions. For the examples developed herein, the L2 coupling produces less error in the zone of interest. The flexibility of the H1 coupling with constant weight function may be beneficial but the results may be affected depending on the topology of the bridging zone. Copyright © 2008 John Wiley & Sons, Ltd. [source] A dual algorithm for the topology optimization of non-linear elastic structuresINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009C. S. Jog Abstract Dual algorithms are ideally suited for the purpose of topology optimization since they work in the space of Lagrange multipliers associated with the constraints. To date, dual algorithms have been applied only for linear structures. Here we extend this methodology to the case of non-linear structures. The perimeter constraint is used to make the topology problem well-posed. We show that the proposed algorithm yields a value of perimeter that is close to that specified by the user. We also address the issue of manufacturability of these designs, by proposing a variant of the standard dual algorithm, which generates designs that are two-dimensional although the loading and the geometry are three-dimensional. Copyright © 2008 John Wiley & Sons, Ltd. [source] Asynchronous multi-domain variational integrators for non-linear problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2008Mark Gates Abstract We develop an asynchronous time integration and coupling method with domain decomposition for linear and non-linear problems in mechanics. To ensure stability in the time integration and in coupling between domains, we use variational integrators with local Lagrange multipliers to enforce continuity at the domain interfaces. The asynchronous integrator lets each domain step with its own time step, using a smaller time step where required by stability and accuracy constraints and a larger time step where allowed. We show that in practice the time step is limited by accuracy requirements rather than by stability requirements. Copyright © 2008 John Wiley & Sons, Ltd. [source] On the L2 and the H1 couplings for an overlapping domain decomposition method using Lagrange multipliersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2007P.-A. Guidault Abstract In this paper, a comparison of the L2 and the H1 couplings is made for an overlapping domain decomposition method using Lagrange multipliers. The analysis of the local equations arising from the formulation of the coupling of two mechanical models shows that continuous weight functions are required for the L2 coupling term whereas both discontinuous and continuous weight functions can be used for the H1 coupling. The choice of the Lagrange multiplier space is discussed and numerically studied. The paper ends with some numerical examples of an end-loaded cantilever beam and a cracked plate under tension and shear. It is shown that the continuity enforced with the H1 coupling leads to a link with a flexibility that can be beneficial for coupling a very coarse mesh with a very fine one. To limit the effect of the volume coupling on the global response, a narrow coupling zone is recommended. In this case, volume coupling tends to a surface coupling, especially with a L2 coupling. Copyright © 2006 John Wiley & Sons, Ltd. [source] Asymptotic numerical methods for unilateral contactINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2006W. Aggoune Abstract New algorithms based upon the asymptotic numerical method (ANM) are proposed to solve unilateral contact problems. ANM leads to a representation of a solution path in terms of series or Padé approximants. To get a smooth solution path, a hyperbolic relation between contact forces and clearance is introduced. Three key points are discussed: the influence of the regularization of the contact law, the discretization of the contact force by Lagrange multipliers and prediction,correction algorithms. Simple benchmarks are considered to evaluate the relevance of the proposed algorithms. Copyright © 2006 John Wiley & Sons, Ltd. [source] Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006Radek Tezaur Abstract Recently, a discontinuous Galerkin finite element method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution in two dimensions of Helmholtz problems in the mid-frequency regime. In this paper, this method is extended to three dimensions and several new elements are proposed. Computational results obtained for several wave guide and acoustic scattering model problems demonstrate one to two orders of magnitude solution time improvement over the higher-order Galerkin method. Copyright © 2005 John Wiley & Sons, Ltd. [source] FETI-DP, BDDC, and block Cholesky methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2006Jing Li Abstract The FETI-DP and BDDC algorithms are reformulated using Block Cholesky factorizations, an approach which can provide a useful framework for the design of domain decomposition algorithms for solving symmetric positive definite linear system of equations. Instead of introducing Lagrange multipliers to enforce the coarse level, primal continuity constraints in these algorithms, a change of variables is used such that each primal constraint corresponds to an explicit degree of freedom. With the new formulation of these algorithms, a simplified proof is provided that the spectra of a pair of FETI-DP and BDDC algorithms, with the same set of primal constraints, are essentially the same. Numerical experiments for a two-dimensional Laplace's equation also confirm this result. Copyright © 2005 John Wiley & Sons, Ltd. [source] Optimal design and optimal control of structures undergoing finite rotations and elastic deformationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004A. Ibrahimbegovic Abstract In this work, we deal with the optimal design and optimal control of structures undergoing large rotations and large elastic deformations. In other words, we show how to find the corresponding initial configuration through optimal design or the corresponding set of multiple load parameters through optimal control, in order to recover a desired deformed configuration or some desirable features of the deformed configuration as specified more precisely by the objective or cost function. The model problem chosen to illustrate the proposed optimal design and optimal control methodologies is the one of geometrically exact beam. First, we present a non-standard formulation of the optimal design and optimal control problems, relying on the method of Lagrange multipliers in order to make the mechanics state variables independent from either design or control variables and thus provide the most general basis for developing the best possible solution procedure. Two different solution procedures are then explored, one based on the diffuse approximation of response function and gradient method and the other one based on genetic algorithm. A number of numerical examples are given in order to illustrate both the advantages and potential drawbacks of each of the presented procedures. Copyright © 2004 John Wiley & Sons, Ltd. [source] | |||||||||||||||||||