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## Newton
Kinds of Newton
Terms modified by Newton
## Selected Abstracts## Ray Tracing Triangular Bézier Patches COMPUTER GRAPHICS FORUM, Issue 3 2001S. H. Martin RothWe present a new approach to finding ray,patch intersections with triangular Bernstein,Bézier patches of arbitrary degree. This paper extends and complements on the short presentation17 . Unlike a previous approach which was based on a combination of hierarchical subdivision and a Newton,like iteration scheme21 , this work adapts the concept of Bézier clipping to the triangular domain. The problem of reporting wrong intersections, inherent to the original Bézier clipping algorithm14 , is inves-tigated and opposed to the triangular case. It turns out that reporting wrong hits is very improbable, even close to impossible, in the triangular set,up. A combination of Bézier clipping and a simple hierarchy of nested bounding volumes offers a reliable and accurate solution to the problem of ray tracing triangular Bézier patches. [source] ## Humphrey Newton (1466,1536): an early Tudor gentleman , By Deborah Youngs ECONOMIC HISTORY REVIEW, Issue 2 2009CHRISTOPHER DYERNo abstract is available for this article. [source] ## A perturbation analysis of harmonic generation from saturated elements in power systems ELECTRICAL ENGINEERING IN JAPAN, Issue 4 2010Teruhisa KumanoAbstract Nonlinear phenomena such as saturation of magnetic flux have considerable effects in power systems analysis. It is reported that a failure in a real 500-kV system triggered islanding operation, where resultant even harmonics caused malfunctions in protective relays. It is also reported that the major origin of this wave distortion is nothing but unidirectional magnetization of the transformer iron core. Time simulation is widely used today to analyze phenomena of this type, but it has basically two shortcomings. One is that the time simulation takes too much computing time in the vicinity of inflection points in the saturation characteristic curve because certain iterative procedures such as N-R (Newton,Raphson) must be used and such methods tend to be caught in an ill-conditioned numerical hunting. The other is that such simulation methods sometimes do not aid an intuitive understanding of the studied phenomenon because all of the nonlinear equations are treated in matrix form and are not properly divided into understandable parts, as is done in linear systems. This paper proposes a new computation scheme that is based on the so-called perturbation method. Magnetic saturation of iron cores in a generator and a transformer are taken into account. The proposed method has a special feature to deal with the first shortcoming of the N-R-based time simulation method stated above. The proposed method does not use an iterative process to reduce the equation residue, but uses perturbation series, so that it is free of the ill-conditioning problem. The user need only calculate the perturbation terms one by one until the necessary accuracy is attained. In a numerical example treated in the present paper, first-order perturbation can achieve reasonably high accuracy, which means very fast computing time. In a numerical study, three nonlinear elements are considered. The calculation results are almost identical to the conventional N-R-based time simulation, which shows the validity of the method. The proposed method can be effectively used in screening where many case studies are needed. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 170(4): 35,42, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20895 [source] ## Newton's treatise on Revelation: the use of a mathematical discourse* HISTORICAL RESEARCH, Issue 204 2006Raquel Delgado-MoreiraThis article focuses on the prophetic work of Newton and his peers, concentrating on a particular manuscript on Revelation for which Newton experimented with a ,mathematical' style. This text exemplifies two distinct levels in Newton's work: structure and epistemology. Since Newton thought that prophecy and mathematics required different kinds of proof, the possible similarities between the two disciplines are not to be found at the level of demonstration. In explaining Newton's use of a mathematical discourse, historians of Newton's writings must give consideration to non-epistemological issues, such as his potential audience and his rhetorical strategies.1 [source] ## Estate Management, Investment and the Gentleman Landlord in Later Medieval England HISTORICAL RESEARCH, Issue 181 2000Deborah YoungsThis article is based on a booklet of accounts for the small estate of Newton, Cheshire. Compiled 1498-1506 by Newton's gentry landlord, they provide rare information on the management and investment strategies of a minor gentleman for his demesne lands. It is to the gentry that historians have generally turned for evidence of enterprise and investment on medieval estates; but few specific examples have been found. This article offers a detailed example supporting the view of the enterprising gentleman, and arguing that a wider diversity of investment was undertaken on a medieval north Midland's estate than is usually appreciated. [source] ## The taxonomic identity of Circus alphonsi (Newton & Gadow 1893), the extinct harrier from Mauritius IBIS, Issue 1 2004Cécile Mourer-ChauviréFirst page of article [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 2009Fushen LiuAbstract 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] ## Coupled HM analysis using zero-thickness interface elements with double nodes. INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 18 2008Part I: Theoretical modelAbstract In recent years, the authors have proposed a new double-node zero-thickness interface element for diffusion analysis via the finite element method (FEM) (Int. J. Numer. Anal. Meth. Geomech. 2004; 28(9): 947,962). In the present paper, that formulation is combined with an existing mechanical formulation in order to obtain a fully coupled hydro-mechanical (or HM) model applicable to fractured/fracturing geomaterials. Each element (continuum or interface) is formulated in terms of the displacements (u) and the fluid pressure (p) at the nodes. After assembly, a particular expression of the traditional ,u,p' system of coupled equations is obtained, which is highly non-linear due to the strong dependence between the permeability and the aperture of discontinuities. The formulation is valid for both pre-existing and developing discontinuities by using the appropriate constitutive model that relates effective stresses to relative displacements in the interface. The system of coupled equations is solved following two different numerical approaches: staggered and fully coupled. In the latter, the Newton,Raphson method is used, and it is shown that the Jacobian matrix becomes non-symmetric due to the dependence of the discontinuity permeability on the aperture. In the part II companion paper (Int. J. Numer. Anal. Meth. Geomech. 2008; DOI: 10.1002/nag.730), the formulation proposed is verified and illustrated with some application examples. 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 2008Angelo AmorosiAbstract 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] ## Analysis of single rock blocks for general failure modes under conservative and non-conservative forces INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2007F. TononAbstract 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] ## An internally consistent integration method for critical state models, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2005Randall J. HickmanAbstract A new procedure to integrate critical state models including Cam,Clay and modified Cam,Clay is proposed here. The proposed procedure makes use of the linearity of the virgin isotropic compression curve and the parallel anisotropic consolidation lines in e,ln p space which are basic features of the formulation of critical state models. Using this algorithm, a unique final stress state may be found as a function of a single unknown for elastoplastic loading. The key equations are given in this article for the Cam,Clay and modified Cam,Clay models. The use of the Newton,Raphson iterative method to minimize residuals and obtain a converged solution is described here. This new algorithm may be applied using the assumptions of linear elasticity or non-linear elasticity within a given loading step. The new algorithm proposed here is internally consistent and has computational advantages over the current numerical integration procedures. Numerical examples are presented to show the performance of the algorithm as compared to other integration algorithms. Published in 2005 by John Wiley & Sons, Ltd. [source] ## A simple robust numerical integration algorithm for a power-law visco-plastic model under both high and low rate-sensitivity INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2004E. A. de Souza NetoAbstract This note describes a simple and extremely robust algorithm for numerical integration of the power-law-type elasto-viscoplastic constitutive model discussed by Peri, (Int. J. Num. Meth. Eng. 1993; 36: 1365,1393). As the rate-independent limit is approached with increasing exponents, the evolution equations of power-law-type models are known to become stiff. Under such conditions, the solution of the implicitly discretized viscoplastic evolution equation cannot be easily obtained by standard root-finding algorithms. Here, a procedure which proves to be remarkably robust under stiff conditions is obtained by means of a simple logarithmic mapping of the basic backward Euler time-discrete equation for the incremental plastic multiplier. The logarithm-transformed equation is solved by the standard Newton,Raphson scheme combined with a simple bisection procedure which ensures that the iterative guesses for the equation unknown (the incremental equivalent plastic strain) remain within the domain where the transformed equation makes sense. The resulting implementation can handle small and large (up to order 106) power-law exponents equally. This allows its effective use under any situation of practical interest, ranging from high rate-sensitivity to virtually rate-independent conditions. The robustness of the proposed scheme is demonstrated by numerical examples. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## A preconditioner freeze strategy for numerical solution of compressible flows INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2003R. S. SilvaAbstract It is well known that Krylov,Schwarz methods are well suited for solving linear systems of equations in high-latency, distributed memory environments and constitute powerful tools when combined with Newton,Krylov methods to solve Computational Fluid Dynamics problems. Nevertheless, the computational costs related to the Jacobian and the preconditioner evaluation can sometimes be prohibitive. In this work a strategy to reduce these costs is presented, based on evaluating a new preconditioner only after it had been frozen for several time steps. Numerical experiments show the computational gain achieved with the proposed strategy. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Simulation of special loading conditions by means of non-linear constraints imposed through Lagrange multipliers INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2002M. A. GutiérrezAbstract 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] ## A contact algorithm for frictional crack propagation with the extended finite element method INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2008Fushen LiuAbstract We present an incremental quasi-static contact algorithm for path-dependent frictional crack propagation in the framework of the extended finite element (FE) method. The discrete formulation allows for the modeling of frictional contact independent of the FE mesh. Standard Coulomb plasticity model is introduced to model the frictional contact on the surface of discontinuity. The contact constraint is borrowed from non-linear contact mechanics and embedded within a localized element by penalty method. Newton,Raphson iteration with consistent linearization is used to advance the solution. We show the superior convergence performance of the proposed iterative method compared with a previously published algorithm called ,LATIN' for frictional crack propagation. Numerical examples include simulation of crack initiation and propagation in 2D plane strain with and without bulk plasticity. In the presence of bulk plasticity, the problem is also solved using an augmented Lagrangian procedure to demonstrate the efficacy and adequacy of the standard penalty solution. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## An incremental formulation for the prediction of two-dimensional fatigue crack growth with curved paths INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2007Ki-Seok KimAbstract This paper presents a new incremental formulation for predicting the curved growth paths of two-dimensional fatigue cracks. The displacement and traction boundary integral equations (BIEs) are employed to calculate responses of a linear elastic cracked body. The Paris law and the principle of local symmetry are adopted for defining the growth rate and direction of a fatigue crack, respectively. The three governing equations, i.e. the BIEs, the Paris law and the local symmetry condition, are non-linear with respect to the crack growth path and unknowns on the boundary. Iterative forms of three governing equations are derived to solve problems of the fatigue crack growth by the Newton,Raphson method. The incremental crack path is modelled as a parabola defined by the crack-tip position, and the trapezoidal rule is employed to integrate the Paris law. The validity of the proposed method is demonstrated by two numerical examples of plates with an edge crack. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## A computational stream function method for two-dimensional incompressible viscous flows INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005Marcelo H. KobayashiAbstract This work concerns the development of a numerical method based on the stream function formulation of the Navier,Stokes equations to simulate two-dimensional,plane or axisymmetric,viscous flows. The main features of the proposed method are: the use of the high order finite-difference compact method for the discretization of the stream function equation, the implicit pseudo-transient Newton,Krylov-multigrid matrix free method for the stationary stream function equation and the fourth order Runge,Kutta method for the integration of non-stationary flows. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005Part I: formulation, benchmarkingAbstract This paper proposes a new technique which allows the use of simplex finite elements (linear triangles in 2D and linear tetrahedra in 3D) in the large strain analysis of nearly incompressible solids. The new technique extends the F-bar method proposed by de Souza Neto et al. (Int. J. Solids and Struct. 1996; 33: 3277,3296) and is conceptually very simple: It relies on the enforcement of (near-) incompressibility over a patch of simplex elements (rather than the point-wise enforcement of conventional displacement-based finite elements). Within the framework of the F-bar method, this is achieved by assuming, for each element of a mesh, a modified (F-bar) deformation gradient whose volumetric component is defined as the volume change ratio of a pre-defined patch of elements. The resulting constraint relaxation effectively overcomes volumetric locking and allows the successful use of simplex elements under finite strain near-incompressibility. As the original F-bar procedure, the present methodology preserves the displacement-based structure of the finite element equations as well as the strain-driven format of standard algorithms for numerical integration of path-dependent constitutive equations and can be used regardless of the constitutive model adopted. The new elements are implemented within an implicit quasi-static environment. In this context, a closed form expression for the exact tangent stiffness of the new elements is derived. This allows the use of the full Newton,Raphson scheme for equilibrium iterations. The performance of the proposed elements is assessed by means of a comprehensive set of benchmarking two- and three-dimensional numerical examples. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Improvement of a frictional contact algorithm for strongly curved contact problems INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2003M. C. OliveiraAbstract One of the challenges in contact problems is the prediction of the actual contact surface and the kind of contact that is established in each region. In numerical simulation of deep drawing problems the contact conditions change continuously during the forming process, increasing the importance of a correct evaluation of these parameters at each load step. In this work a new contact search algorithm devoted to contact between a deformable and a rigid body is presented. The rigid body is modelled by parametric Bézier surfaces, whereas the deformable body is discretized with finite elements. The numerical schemes followed rely on a frictional contact algorithm that operates directly on the parametric Bézier surfaces. The algorithm is implemented in the deep drawing implicit finite element code DD3IMP. This code uses a mechanical model that takes into account the large elastoplastic strains and rotations. The Coulomb classical law models the frictional contact problem, which is treated with an augmented Lagrangian approach. A fully implicit algorithm of Newton,Raphson type is used to solve within a single iterative loop the non-linearities related with the frictional contact problem and the elastoplastic behaviour of the deformable body. The numerical simulations presented demonstrate the performance of the contact search algorithm in an example with complex tools geometry. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Efficient implicit finite element analysis of sheet forming processes INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003A. H. van den BoogaardAbstract The computation time for implicit finite element analyses tends to increase disproportionally with increasing problem size. This is due to the repeated solution of linear sets of equations, if direct solvers are used. By using iterative linear equation solvers the total analysis time can be reduced for large systems. For plate or shell element models, however, the condition of the matrix is so ill that iterative solvers do not reach the huge time-savings that are realized with solid elements. By introducing inertial effects into the implicit finite element code the condition number can be improved and iterative solvers perform much better. An additional advantage is that the inertial effects stabilize the Newton,Raphson iterations. This also applies to quasi-static processes, for which the inertial effects finally do not affect the results. The presented method can readily be implemented in existing implicit finite element codes. Industrial size deep drawing simulations are executed to investigate the performance of the recommended strategy. It is concluded that the computation time is decreased by a factor of 5 to 10. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Stabilized finite element method for viscoplastic flow: formulation with state variable evolution INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003Antoinette M. ManiattyAbstract A stabilized, mixed finite element formulation for modelling viscoplastic flow, which can be used to model approximately steady-state metal-forming processes, is presented. The mixed formulation is expressed in terms of the velocity, pressure and state variable fields, where the state variable is used to describe the evolution of the material's resistance to plastic flow. The resulting system of equations has two sources of well-known instabilities, one due to the incompressibility constraint and one due to the convection-type state variable equation. Both of these instabilities are handled by adding mesh-dependent stabilization terms, which are functions of the Euler,Lagrange equations, to the usual Galerkin method. Linearization of the weak form is derived to enable a Newton,Raphson implementation into an object-oriented finite element framework. A progressive solution strategy is used for improving convergence for highly non-linear material behaviour, typical for metals. Numerical experiments using the stabilization method with hierarchic shape functions for the velocity, pressure and state variable fields in viscoplastic flow and metal-forming problems show that the stabilized finite element method is effective and efficient for non-linear steady forming problems. Finally, the results are discussed and conclusions are inferred. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## A variational multiscale Newton,Schur approach for the incompressible Navier,Stokes equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2010D. Z. TurnerAbstract In the following paper, we present a consistent Newton,Schur (NS) solution approach for variational multiscale formulations of the time-dependent Navier,Stokes equations in three dimensions. The main contributions of this work are a systematic study of the variational multiscale method for three-dimensional problems and an implementation of a consistent formulation suitable for large problems with high nonlinearity, unstructured meshes, and non-symmetric matrices. In addition to the quadratic convergence characteristics of a Newton,Raphson-based scheme, the NS approach increases computational efficiency and parallel scalability by implementing the tangent stiffness matrix in Schur complement form. As a result, more computations are performed at the element level. Using a variational multiscale framework, we construct a two-level approach to stabilizing the incompressible Navier,Stokes equations based on a coarse and fine-scale subproblem. We then derive the Schur complement form of the consistent tangent matrix. We demonstrate the performance of the method for a number of three-dimensional problems for Reynolds number up to 1000 including steady and time-dependent flows. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## PID adaptive control of incremental and arclength continuation in nonlinear applications INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2009A. M. P. ValliAbstract A proportional-integral-derivative (PID) control approach is developed, implemented and investigated numerically in conjunction with continuation techniques for nonlinear problems. The associated algorithm uses PID control to adapt parameter stepsize for branch,following strategies such as those applicable to turning point and bifurcation problems. As representative continuation strategies, incremental Newton, Euler,Newton and pseudo-arclength continuation techniques are considered. Supporting numerical experiments are conducted for finite element simulation of the ,driven cavity' Navier,Stokes benchmark over a range in Reynolds number, the classical Bratu turning point problem over a reaction parameter range, and for coupled fluid flow and heat transfer over a range in Rayleigh number. Computational performance using PID stepsize control in conjunction with inexact Newton,Krylov solution for coupled flow and heat transfer is also examined for a 3D test case. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## A comparative study of GLS finite elements with velocity and pressure equally interpolated for solving incompressible viscous flows INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2009Yongtao WeiAbstract A comparative study of the bi-linear and bi-quadratic quadrilateral elements and the quadratic triangular element for solving incompressible viscous flows is presented. These elements make use of the stabilized finite element formulation of the Galerkin/least-squares method to simulate the flows, with the pressure and velocity fields interpolated with equal orders. The tangent matrices are explicitly derived and the Newton,Raphson algorithm is employed to solve the resulting nonlinear equations. The numerical solutions of the classical lid-driven cavity flow problem are obtained for Reynolds numbers between 1000 and 20 000 and the accuracy and converging rate of the different elements are compared. The influence on the numerical solution of the least square of incompressible condition is also studied. The numerical example shows that the quadratic triangular element exhibits a better compromise between accuracy and converging rate than the other two elements. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Temporal accuracy analysis of phase change convection simulations using the JFNK-SIMPLE algorithm INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2007Katherine J. EvansAbstract The incompressible Navier,Stokes and energy conservation equations with phase change effects are applied to two benchmark problems: (1) non-dimensional freezing with convection; and (2) pure gallium melting. Using a Jacobian-free Newton,Krylov (JFNK) fully implicit solution method preconditioned with the SIMPLE (Numerical Heat Transfer and Fluid Flow. Hemisphere: New York, 1980) algorithm using centred discretization in space and three-level discretization in time converges with second-order accuracy for these problems. In the case of non-dimensional freezing, the temporal accuracy is sensitive to the choice of velocity attenuation parameter. By comparing to solutions with first-order backward Euler discretization in time, it is shown that the second-order accuracy in time is required to resolve the fine-scale convection structure during early gallium melting. Qualitative discrepancies develop over time for both the first-order temporal discretized simulation using the JFNK-SIMPLE algorithm that converges the nonlinearities and a SIMPLE-based algorithm that converges to a more common mass balance condition. The discrepancies in the JFNK-SIMPLE simulations using only first-order rather than second-order accurate temporal discretization for a given time step size appear to be offset in time. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Application of second-order adjoint technique for conduit flow problem INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2007T. KurahashiAbstract 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] ## Continuation of travelling-wave solutions of the Navier,Stokes equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2006Isabel MercaderAbstract An efficient way of obtaining travelling waves in a periodic fluid system is described and tested. We search for steady states in a reference frame travelling at the wave phase velocity using a first-order pseudospectral semi-implicit time scheme adapted to carry out the Newton's iterations. The method is compared to a standard Newton,Raphson solver and is shown to be highly efficient in performing this task, even when high-resolution grids are used. This method is well suited to three-dimensional calculations in cylindrical or spherical geometries. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Hierarchic multigrid iteration strategy for the discontinuous Galerkin solution of the steady Euler equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9-10 2006Koen HillewaertAbstract We study the efficient use of the discontinuous Galerkin finite element method for the computation of steady solutions of the Euler equations. In particular, we look into a few methods to enhance computational efficiency. In this context we discuss the applicability of two algorithmical simplifications that decrease the computation time associated to quadrature. A simplified version of the quadrature free implementation applicable to general equations of state, and a simplified curved boundary treatment are investigated. We as well investigate two efficient iteration techniques, namely the classical Newton,Krylov method used in computational fluid dynamics codes, and a variant of the multigrid method which uses interpolation orders rather than coarser tesselations to define the auxiliary coarser levels. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Iterative solution techniques for unsteady flow computations using higher order time integration schemes INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8-9 2005H. BijlAbstract In this paper iterative techniques for unsteady flow computations with implicit higher order time integration methods at large time steps are investigated. It is shown that with a minimal coding effort the standard non-linear multigrid method can be combined with a Newton,Krylov method leading to speed-ups in the order of 30%. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Speed-up and performance evaluation of piecewise-linear DC analysis INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 4 2007Janne RoosArticle first published online: 29 NOV 200Abstract The good convergence properties of piecewise-linear (PWL) DC analysis have been thoroughly discussed in many papers. This paper, in turn, concentrates on the speed of PWL DC analysis, where the boundary crossing of linear regions plays a crucial role. Fast methods are presented for performing the following boundary-crossing computations: LU-decomposition update, matrix-equation solution, boundary-crossing direction, and damping-factor determination. Special attention is given to those PWL DC analysis methods that perform PWL modelling of the non-linear components on the fly; an adaptive method is proposed for controlling the accuracy of PWL modelling and speeding up simulation. The computational efficiency of the accelerated PWL DC analysis is discussed and compared with that of conventional, Newton,Raphson iteration-based, DC analysis. Finally, the performance evaluation is completed with realistic simulation examples: it is demonstrated that the speed of the accelerated PWL DC analysis is comparable with that of the conventional DC analysis. Copyright © 2006 John Wiley & Sons, Ltd. [source] |