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Iterative Scheme (iterative + scheme)
Selected AbstractsAn extended finite element framework for slow-rate frictional faulting with bulk plasticity and variable frictionINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2009Fushen 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] Generalized trapezoidal numerical integration of an advanced soil modelINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2008Yunming Yang Abstract This paper investigates the numerical performance of the generalized trapezoidal integration rule by using an advanced soil model. The generalized trapezoidal integration rule can include many other integration algorithms by adjusting a single parameter , ranging from 1 to 0. The soil model used is the recently developed middle surface concept (MSC) sand model which simulates different soil response characteristics by using different pseudo-yield functions. The generalized trapezoidal rule and MSC sand model are used to simulate the responses of sand samples with different relative densities under various initial and loading conditions. Instead of a single step, multiple loading steps bring the sample to the vicinity of failure. These comprehensive investigations examine and compare the influences of various values of , on the numerical solution of integrated constitutive equations, the convergence of Newton's iterative scheme, and the integration accuracy. Copyright © 2007 John Wiley & Sons, Ltd. [source] Analysis of single rock blocks for general failure modes under conservative and non-conservative forcesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2007F. Tonon Abstract After describing the kinematics of a generic rigid block subjected to large rotations and displacements, the Udwadia's General Principle of Mechanics is applied to the dynamics of a rigid block with frictional constraints to show that the reaction forces and moments are indeterminate. Thus, the paper presents an incremental-iterative algorithm for analysing general failure modes of rock blocks subject to generic forces, including non-conservative forces such as water forces. Consistent stiffness matrices have been developed that fully exploit the quadratic convergence of the adopted Newton,Raphson iterative scheme. The algorithm takes into account large block displacements and rotations, which together with non-conservative forces make the stiffness matrix non-symmetric. Also included in the algorithm are in situ stress and fracture dilatancy, which introduces non-symmetric rank-one modifications to the stiffness matrix. Progressive failure is captured by the algorithm, which has proven capable of detecting numerically challenging failure modes, such as rotations about only one point. Failure modes may originate from a limit point or from dynamic instability (divergence or flutter); equilibrium paths emanating from bifurcation points are followed by the algorithm. The algorithm identifies both static and dynamic failure modes. The calculation of the factor of safety comes with no overhead. Examples show the equilibrium path of a rock block that undergoes slumping failure must first pass through a bifurcation point, unless the block is laterally constrained. Rock blocks subjected to water forces (or other non-conservative forces) may undergo flutter failure before reaching a limit point. Copyright © 2007 John Wiley & Sons, Ltd. [source] A non-iterative derivation of the common plane for contact detection of polyhedral blocksINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008Shu-Wei Chang Abstract A non-iterative derivation for finding the common plane between two polyhedral blocks is presented. By exploiting geometric relations between the normal of a plane and the closest vertex on a block, the common plane can be resolved without resorting to an iterative method. To facilitate derivations, normals in half-space are decomposed into finite subsets in which each subset corresponds to the same closest vertex on a block. The gap function, originally dependent on the normal and the two closest vertices, becomes a function of the normal only. To compute the gap for a given normal subset, the maximum theorem and the maximum projection theorem are introduced. The maximum theorem reduces finding the maximum in a subset to its boundary. Calculating the gap in 2D in a given subset thus reduces to checking two inner products. The maximum projection theorem further reduces finding the maximum on a 3D boundary to an explicit form. Three numerical examples are used to demonstrate the accuracy and efficiency of the proposed scheme. The example in which the blocks are in contact further shows the existence of a local maximum while calculating the gap and illustrates the potential deficiencies in using the Cundall's iterative scheme. Copyright © 2007 John Wiley & Sons, Ltd. [source] Optimized damage detection of steel plates from noisy impact testINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2006G. Rus Abstract Model-based non-destructive evaluation proceeds measuring the response after an excitation on an accessible area of the structure. The basis for processing this information has been established in recent years as an iterative scheme that minimizes the discrepancy between this experimental measurement and sequence of measurement trials predicted by a numerical model. The unknown damage that minimizes this discrepancy by means of a cost functional is to be found. The damage location and size is quantified and sought by means of a well-conditioned parametrization. The design of the magnitude to measure, its filtering for reducing noise effects and calibration, as well as the design of the cost functional and parametrization, determines the robustness of the search to combat noise and other uncertainty factors. These are key open issues to improve the sensitivity and identifiability during the information processing. Among them, a filter for the cost functional is proposed in this study for maximal sensitivity to the damage detection of steel plate under the impact loading. This filter is designed by means of a wavelet decomposition together with a selection of the measuring points, and the optimization criterion is built on an estimate of the probability of detection, using genetic algorithms. Numerical examples show that the use of the optimal filter allows to find damage of a magnitude several times smaller. Copyright © 2006 John Wiley & Sons, Ltd. [source] A Petrov,Galerkin finite element model for one-dimensional fully non-linear and weakly dispersive wave propagationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2001Seung-Buhm Woo Abstract A new finite element method is presented to solve one-dimensional depth-integrated equations for fully non-linear and weakly dispersive waves. For spatial integration, the Petrov,Galerkin weighted residual method is used. The weak forms of the governing equations are arranged in such a way that the shape functions can be piecewise linear, while the weighting functions are piecewise cubic with C2 -continuity. For the time integration an implicit predictor,corrector iterative scheme is employed. Within the framework of linear theory, the accuracy of the scheme is discussed by considering the truncation error at a node. The leading truncation error is fourth-order in terms of element size. Numerical stability of the scheme is also investigated. If the Courant number is less than 0.5, the scheme is unconditionally stable. By increasing the number of iterations and/or decreasing the element size, the stability characteristics are improved significantly. Both Dirichlet boundary condition (for incident waves) and Neumann boundary condition (for a reflecting wall) are implemented. Several examples are presented to demonstrate the range of applicabilities and the accuracy of the model. Copyright © 2001 John Wiley & Sons, Ltd. [source] Boundary element analysis of driven cavity flow for low and moderate Reynolds numbersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2001M. Aydin Abstract A boundary element method for steady two-dimensional low-to-moderate-Reynolds number flows of incompressible fluids, using primitive variables, is presented. The velocity gradients in the Navier,Stokes equations are evaluated using the alternatives of upwind and central finite difference approximations, and derivatives of finite element shape functions. A direct iterative scheme is used to cope with the non-linear character of the integral equations. In order to achieve convergence, an underrelaxation technique is employed at relatively high Reynolds numbers. Driven cavity flow in a square domain is considered to validate the proposed method by comparison with other published data. Copyright © 2001 John Wiley & Sons, Ltd. [source] A combined iterative scheme for identification and control redesignsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 8 2004Paresh Date Abstract This work proposes a unified algorithm for identification and control. Frequency domain data of the plant is weighted to satisfy the given performance specifications. A model is then identified from this weighted frequency domain data and a controller is synthesised using the ,, loopshaping design procedure. The cost function used in the identification stage essentially minimizes a tight upper bound on the difference between the achieved and the designed performance in the sense of the ,, loopshaping design paradigm. Given a model, a method is also suggested to re-adjust model and weighting transfer functions to reduce further the worst case chordal distance between the weighted true plant and the model. Copyright © 2004 John Wiley & Sons, Ltd. [source] Flows through horizontal channels of porous materialsINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 10 2003A.K. Al-Hadhrami Abstract In this paper, the control volume method (CVM) with the staggered grid system is utilized to solve the two-dimensional Brinkman equation for different configurations of porous media in a horizontal channel. The values of the permeability of sand and clear fluid are considered when performing several numerical investigations which enable the evaluation of the behaviour of the flow through regions that mathematically model some geological features (faults/fractures) present in oil reservoirs or groundwater flows. We have found that the convergence of the CVM can be achieved within a reasonable number of iterations when there is a gap present between a partial barrier of low Darcy number and the channel boundary. However, a complete barrier across the channel results in a very high resistance and hence there is a large pressure drop which causes difficulties in convergence. In order to improve the rate of convergence in such situations, an average pressure correction (APC) technique, which is based on global mass conservation, is developed. The use of this technique, along with the CVM, can rapidly build up the pressure drop across such a barrier and hence dramatically improve the rate of convergence of the iterative scheme. Copyright © 2003 John Wiley & Sons, Ltd. [source] A low complexity partially adaptive CDMA receiver for downlink mobile satellite communicationsINTERNATIONAL JOURNAL OF SATELLITE COMMUNICATIONS AND NETWORKING, Issue 1 2003Gau-Joe Lin Abstract A novel CDMA receiver with enhanced interference suppression is proposed for pilot symbols assisted mobile satellite systems in the presence of frequency offset. The design of the receiver involves the following procedure. First, adaptive correlators are constructed at different fingers, based on the scheme of generalized sidelobe canceller (GSC), to collect the multipath signals and suppress multi-access interference (MAI). In particular, a partially adaptive (PA) realization of the GSC correlators is proposed based on the Krylov subspace technique, leading to an efficient algorithm without the need of complicated matrix computations. Second, pilot symbols assisted frequency offset estimation, channel estimation and RAKE combining give the estimate of signal symbols. Finally, further performance enhancement is achieved by an iterative scheme in which the signal is reconstructed and subtracted from the GSC correlators input, leading to faster convergence of the receiver. The proposed low complexity PA receiver is suitable or the downlink of mobile satellite CDMA systems, and shown to outperform the conventional fully adaptive MMSE receiver by using a small number of pilot symbols. Copyright © 2003 John Wiley & Sons, Ltd. [source] Quick scheme for evaluation of atomic charges in arbitrary aluminophosphate sieves on the basis of electron densities calculated with DFT methodsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 10 2007A. V. Larin Abstract It is demonstrated that unique and simple analytical functions are justified for the atomic charge dependences q of the T (T = Al, P) and O atoms of aluminophosphates (AlPOs) using DFT calculations with several basis sets, starting from STO-3G to 3-21G and 6-21G**. Three internal (bonds, angles, ,) coordinates for the charge dependences of the T atoms and four coordinates for the O are sufficient to reach a precision of 1.8% for the fitted q(Al), 1.0% for q(P), and 2.5% for q(O) relatively to the values calculated at any basis set level. The proposed strategy consists in an iterative scheme starting from charge dependences based on the neighbor's positions only. Electrostatic potential values are computed to illustrate the differences between the calculated and fitted charges in the considered AlPO models. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007 [source] Treating missing values in INAR(1) models: An application to syndromic surveillance dataJOURNAL OF TIME SERIES ANALYSIS, Issue 1 2010Jonas Andersson Time-series models for count data have found increased interest in recent years. The existing literature refers to the case of data that have been fully observed. In this article, methods for estimating the parameters of the first-order integer-valued autoregressive model in the presence of missing data are proposed. The first method maximizes a conditional likelihood constructed via the observed data based on the k -step-ahead conditional distributions to account for the gaps in the data. The second approach is based on an iterative scheme where missing values are imputed so as to update the estimated parameters. The first method is useful when the predictive distributions have simple forms. We derive in full details this approach when the innovations are assumed to follow a finite mixture of Poisson distributions. The second method is applicable when there are no closed form expression for the conditional likelihood or they are hard to derive. The proposed methods are applied to a dataset concerning syndromic surveillance during the Athens 2004 Olympic Games. [source] Reconstruction of MR images from data acquired on an arbitrary k -space trajectory using the same-image weightMAGNETIC RESONANCE IN MEDICINE, Issue 2 2002Yongxian Qian Abstract A sampling density compensation function denoted "same-image (SI) weight" is proposed to reconstruct MR images from the data acquired on an arbitrary k -space trajectory. An equation for the SI weight is established on the SI criterion and an iterative scheme is developed to find the weight. The SI weight is then used to reconstruct images from the data calculated on a random trajectory in a numerical phantom case and from the data acquired on interleaved spirals in an in vivo experiment, respectively. In addition, Pipe and Menon's weight (MRM 1999;41:179,186) is also used in the reconstructions to make a comparison. The images obtained with the SI weight were found to be slightly more accurate than those obtained with Pipe's weight. Magn Reson Med 48:306,311, 2002. © 2002 Wiley-Liss, Inc. [source] First-order system least squares for the Oseen equationsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 7 2006Sang Dong Kim Abstract Following earlier work for Stokes equations, a least squares functional is developed for two- and three-dimensional Oseen equations. By introducing a velocity flux variable and associated curl and trace equations, ellipticity is established in an appropriate product norm. The form of Oseen equations examined here is obtained by linearizing the incompressible Navier,Stokes equations. An algorithm is presented for approximately solving steady-state, incompressible Navier,Stokes equations with a nested iteration-Newton-FOSLS-AMG iterative scheme, which involves solving a sequence of Oseen equations. Some numerical results for Kovasznay flow are provided. Copyright © 2006 John Wiley & Sons, Ltd. [source] Algebraic preconditioning versus direct solvers for dense linear systems as arising in crack propagation problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2005Erik Bängtsson Abstract Preconditioned iterative solution methods are compared with the direct Gaussian elimination method to solve dense linear systems Ax=b which originate from problems, discretized by boundary element method (BEM) techniques. Numerical experiments are presented and compared with the direct solution method available in a commercial BEM package, which show that the preconditioned iterative schemes are highly competitive with respect to both arithmetic operations required and memory demands. Copyright © 2004 John Wiley & Sons, Ltd. [source] An unconditionally convergent algorithm for the evaluation of the ultimate limit state of RC sections subject to axial force and biaxial bendingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2007G. Alfano Abstract We present a numerical procedure, based upon a tangent approach, for evaluating the ultimate limit state (ULS) of reinforced concrete (RC) sections subject to axial force and biaxial bending. The RC sections are assumed to be of arbitrary polygonal shape and degree of connection; furthermore, it is possible to keep fixed a given amount of the total load and to find the ULS associated only with the remaining part which can be increased by means of a load multiplier. The solution procedure adopts two nested iterative schemes which, in turn, update the current value of the tentative ultimate load and the associated strain parameters. In this second scheme an effective integration procedure is used for evaluating in closed form, as explicit functions of the position vectors of the vertices of the section, the domain integrals appearing in the definition of the tangent matrix and of the stress resultants. Under mild hypotheses, which are practically satisfied for all cases of engineering interest, the existence and uniqueness of the ULS load multiplier is ensured and the global convergence of the proposed solution algorithm to such value is proved. An extensive set of numerical tests, carried out for rectangular, L-shaped and multicell sections shows the effectiveness of the proposed solution procedure. Copyright © 2007 John Wiley & Sons, Ltd. [source] Numerical analysis of Augmented Lagrangian algorithms in complementary elastoplasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004L. Contrafatto The main subject of the paper is the investigation of Augmented Lagrangian algorithms and update formulas in the solution of elastoplastic problems. A stress rate formulation for elastoplastic models with internal variables and its finite increment form is employed to state the mechanical problem. In this formulation the Augmented Lagrangian is used to enforce the constraint of plastic admissibility directly on the stresses and thermodynamic forces. This is not a limitation of the Augmented Lagrangian approach, and the same framework can be built on more classical displacement formulations as well. The meaning and the derivation of various first and second order Lagrangian multipliers update formulas and iterative schemes is shown. A new diagonal iteration algorithm and the introduction of a scale factor for the Augmented Lagrangian term are proposed. Numerical examples compare the efficiency of several forms of Augmented Lagrangian algorithms and illustrate the influence of the scale factor and of the penalty parameter. Copyright © 2004 John Wiley & Sons, Ltd. [source] Implementation of a stabilized finite element formulation for the incompressible Navier,Stokes equations based on a pressure gradient projectionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2001Ramon Codina Abstract We discuss in this paper some implementation aspects of a finite element formulation for the incompressible Navier,Stokes equations which allows the use of equal order velocity,pressure interpolations. The method consists in introducing the projection of the pressure gradient and adding the difference between the pressure Laplacian and the divergence of this new field to the incompressibility equation, both multiplied by suitable algorithmic parameters. The main purpose of this paper is to discuss how to deal with the new variable in the implementation of the algorithm. Obviously, it could be treated as one extra unknown, either explicitly or as a condensed variable. However, we take for granted that the only way for the algorithm to be efficient is to uncouple it from the velocity,pressure calculation in one way or another. Here we discuss some iterative schemes to perform this uncoupling of the pressure gradient projection (PGP) from the calculation of the velocity and the pressure, both for the stationary and the transient Navier,Stokes equations. In the first case, the strategies analyzed refer to the interaction of the linearization loop and the iterative segregation of the PGP, whereas in the second the main dilemma concerns the explicit or implicit treatment of the PGP. Copyright © 2001 John Wiley & Sons, Ltd. [source] On a third-order Newton-type method free of bilinear operatorsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2010S. Amat Abstract This paper is devoted to the study of a third-order Newton-type method. The method is free of bilinear operators, which constitutes the main limitation of the classical third-order iterative schemes. First, a global convergence theorem in the real case is presented. Second, a semilocal convergence theorem and some examples are analyzed, including quadratic equations and integral equations. Finally, an approximation using divided differences is proposed and used for the approximation of boundary-value problems. Copyright © 2009 John Wiley & Sons, Ltd. [source] Iterative versus direct parallel substructuring methods in semiconductor device modellingNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2005L. Giraud Abstract The numerical simulation of semiconductor devices is extremely demanding in term of computational time because it involves complex embedded numerical schemes. At the kernel of these schemes is the solution of very ill-conditioned large linear systems. In this paper, we present the various ingredients of some hybrid iterative schemes that play a central role in the robustness of these solvers when they are embedded in other numerical procedures. On a set of two-dimensional unstructured mixed finite element problems representative of semiconductor simulation, we perform a fair and detailed comparison between parallel iterative and direct linear solution techniques. We show that iterative solvers can be robust enough to solve the very challenging linear systems that arise in those simulations. Copyright © 2004 John Wiley & Sons, Ltd. [source] Numerical methods for fourth-order nonlinear elliptic boundary value problemsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2001C. V. Pao Abstract The aim of this article is to present several computational algorithms for numerical solutions of a nonlinear finite difference system that represents a finite difference approximation of a class of fourth-order elliptic boundary value problems. The numerical algorithms are based on the method of upper and lower solutions and its associated monotone iterations. Three linear monotone iterative schemes are given, and each iterative scheme yields two sequences, which converge monotonically from above and below, respectively, to a maximal solution and a minimal solution of the finite difference system. This monotone convergence property leads to upper and lower bounds of the solution in each iteration as well as an existence-comparison theorem for the finite difference system. Sufficient conditions for the uniqueness of the solution and some techniques for the construction of upper and lower solutions are obtained, and numerical results for a two-point boundary-value problem with known analytical solution are given. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:347,368, 2001 [source] | ||||||||||||||||