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Newton Algorithm (newton + algorithm)

Distribution by Scientific Domains
Engineering75%

Selected Abstracts

Dynamic Wavelet Neural Network for Nonlinear Identification of Highrise Buildings

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 5 2005
Xiaomo Jiang
Compared with conventional neural networks, training of a dynamic neural network for system identification of large-scale structures is substantially more complicated and time consuming because both input and output of the network are not single valued but involve thousands of time steps. In this article, an adaptive Levenberg,Marquardt least-squares algorithm with a backtracking inexact linear search scheme is presented for training of the dynamic fuzzy WNN model. The approach avoids the second-order differentiation required in the Gauss,Newton algorithm and overcomes the numerical instabilities encountered in the steepest descent algorithm with improved learning convergence rate and high computational efficiency. The model is applied to two highrise moment-resisting building structures, taking into account their geometric nonlinearities. Validation results demonstrate that the new methodology provides an efficient and accurate tool for nonlinear system identification of high-rising buildings. [source]

Geometry update driven by material forces for simulation of brittle crack growth in functionally graded materials

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2009
Rolf Mahnken
Abstract Functionally graded materials (FGMs) are advanced materials that possess continuously graded properties, such that the growth of cracks is strongly dependent on the gradation of the material. In this work a thermodynamic consistent framework for crack propagation in FGMs is presented, by applying a dissipation inequality to a time-dependent migrating control volume. The direction of crack growth is obtained in terms of material forces as a result of the principle of maximum dissipation. In the numerical implementation a staggered algorithm,deformation update for fixed geometry followed by geometry update for fixed deformation,is employed within each time increment. The geometry update is a result of the incremental crack propagation, which is driven by material forces. The corresponding mesh is generated by combining Delaunay triangulation with local mesh refinement. Furthermore a Newton algorithm is proposed, taking into account mesh transfer of displacements for crack propagation in incremental elasticity. In two numerical examples brittle crack propagation in FGMs is investigated for various directions of strength gradation within the structures. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A 3D incompressible Navier,Stokes velocity,vorticity weak form finite element algorithm

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2002
K. L. Wong
Abstract The velocity,vorticity formulation is selected to develop a time-accurate CFD finite element algorithm for the incompressible Navier,Stokes equations in three dimensions. The finite element implementation uses equal order trilinear finite elements on a non-staggered hexahedral mesh. A second order vorticity kinematic boundary condition is derived for the no slip wall boundary condition which also enforces the incompressibility constraint. A biconjugate gradient stabilized (BiCGSTAB) sparse iterative solver is utilized to solve the fully coupled system of equations as a Newton algorithm. The solver yields an efficient parallel solution algorithm on distributed-memory machines, such as the IBM SP2. Three dimensional laminar flow solutions for a square channel, a lid-driven cavity, and a thermal cavity are established and compared with available benchmark solutions. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Dynamic Newton,gradient-direction-type algorithm for multilayer structure determination using grazing X-ray specular scattering: numerical simulation and analysis

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2009
F. N. Chukhovskii
A new dynamic iterative algorithm code for retrieving macroscopic multilayer structure parameters (the layer thickness and complex refraction index for each layer, the surface roughness and the interface roughness between the layers) from specular scattering angular scan data is proposed. The use of conventional direct methods, particularly the well known Newton algorithm and gradient-direction-type algorithm operating dynamically to minimize the error functional in a least-squares fashion, is explored. Such an approach works well and seems to be effective in solving the inverse problem in the high-resolution X-ray reflectometry (HRXR) method. In order to demonstrate some features of the proposed iterative algorithm, numerical calculations for retrieving three-layer structure parameters are carried out using simulated HRXR angular scan data. The calculations indicate clearly that the dynamic iterative algorithm is convergent and capable of yielding the true solution. It is important that the performance coefficient for successful iterative cycles for the absolute minimization of the HRXR error functional is quite high even if the initial values of the search parameters are chosen rather far from the true values. It is particularly noteworthy that the relative number of successful iterative cycles is of the order of 90,40% when only moderately accurate initial parameter values, varying by ±10,40% from the true values, are presumed. [source]