Newton Iterations (newton + iteration)

Distribution by Scientific Domains

Selected Abstracts

A rate-dependent cohesive crack model based on anisotropic damage coupled to plasticity

Per-Ola Svahn
Abstract In quasi-brittle material the complex process of decohesion between particles in microcracks and localization of the displacement field into macrocracks is limited to a narrow fracture zone, and it is often modelled with cohesive crack models. Since the anisotropic nature of the decohesion process in separation and sliding is essential, it is particularly focused in this paper. Moreover, for cyclic and dynamic loading the unloading, load reversal (including crack closure) and rate dependency are essential features that are included in a new model. The modelling of degradation is based on a ,localized' version of anisotropic continuum damage coupled to inelasticity. The concept of strain energy equivalence between the states in the effective and nominal settings is adopted in order to define the free energy of the interface. The proposed fracture criterion is of the Mohr type, with a smooth transition of the failure and kinematics (slip and dilatation) characteristics between tension and shear. The chosen potential, of the Lemaitre-type, for evolution of the dissipative processes is additively decomposed into plastic and damage parts, and non-associative constitutive equations are obtained. The constitutive equations are integrated by applying the backward Euler rule and by using Newton iteration. The proposed model is assessed analytically and numerically and a typical calibration procedure for concrete is proposed. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Modular solvers for image restoration problems using the discrepancy principle

Peter Blomgren
Abstract Many problems in image restoration can be formulated as either an unconstrained non-linear minimization problem, usually with a Tikhonov -like regularization, where the regularization parameter has to be determined; or as a fully constrained problem, where an estimate of the noise level, either the variance or the signal-to-noise ratio, is available. The formulations are mathematically equivalent. However, in practice, it is much easier to develop algorithms for the unconstrained problem, and not always obvious how to adapt such methods to solve the corresponding constrained problem. In this paper, we present a new method which can make use of any existing convergent method for the unconstrained problem to solve the constrained one. The new method is based on a Newton iteration applied to an extended system of non-linear equations, which couples the constraint and the regularized problem, but it does not require knowledge of the Jacobian of the irregularity functional. The existing solver is only used as a black box solver, which for a fixed regularization parameter returns an improved solution to the unconstrained minimization problem given an initial guess. The new modular solver enables us to easily solve the constrained image restoration problem; the solver automatically identifies the regularization parameter, during the iterative solution process. We present some numerical results. The results indicate that even in the worst case the constrained solver requires only about twice as much work as the unconstrained one, and in some instances the constrained solver can be even faster. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A new damage model based on non-local displacements

Antonio Rodríguez-Ferran
Abstract A new non-local damage model is presented. Non-locality (of integral or gradient type) is incorporated into the model by means of non-local displacements. This contrasts with existing damage models, where a non-local strain or strain-related state variable is used. The new model is very attractive from a computational viewpoint, especially regarding the computation of the consistent tangent matrix needed to achieve quadratic convergence in Newton iterations. At the same time, its physical response is very similar to that of the standard models, including its regularization capabilities. All these aspects are discussed in detail and illustrated by means of numerical examples. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Toward large scale F.E. computation of hot forging process using iterative solvers, parallel computation and multigrid algorithms

K. Mocellin
Abstract The industrial simulation code Forge3® is devoted to three-dimensional metal forming applications. This finite element software is based on an implicit approach. It is able to carry out the large deformations of viscoplastic incompressible materials with unilateral contact conditions. The finite element discretization is based on a stable mixed velocity,pressure formulation and tetrahedral unstructured meshes. Central to the Newton iterations dealing with the non-linearities, a preconditioned conjugate residual method (PCR) is used. The parallel version of the code uses an SPMD programming model and several results on complex applications have been published. In order to reduce the CPU time computation, a new solver has been developed which is based on multigrid theory. A detailed presentation of the different elements of the method is given: the geometrical approach based on embedded meshes, the direct resolution of the velocity,pressure system, the use of PCR method as an original smoother and for solving the coarse problem, the full multigrid method and the required preconditioning by an incomplete Cholesky factorization for problems with complex contact conditions. By considering different forging cases, the theoretical properties of the multigrid method are numerically verified, optimizations of the solver are presented and finally, the results obtained on several industrial problems are given, showing the efficiency of the new solver that provides speed-up larger than 5. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Radial basis collocation method and quasi-Newton iteration for nonlinear elliptic problems

H.Y. Hu
Abstract This work presents a radial basis collocation method combined with the quasi-Newton iteration method for solving semilinear elliptic partial differential equations. The main result in this study is that there exists an exponential convergence rate in the radial basis collocation discretization and a superlinear convergence rate in the quasi-Newton iteration of the nonlinear partial differential equations. In this work, the numerical error associated with the employed quadrature rule is considered. It is shown that the errors in Sobolev norms for linear elliptic partial differential equations using radial basis collocation method are bounded by the truncation error of the RBF. The combined errors due to radial basis approximation, quadrature rules, and quasi-Newton and Newton iterations are also presented. This result can be extended to finite element or finite difference method combined with any iteration methods discussed in this work. The numerical example demonstrates a good agreement between numerical results and analytical predictions. The numerical results also show that although the convergence rate of order 1.62 of the quasi-Newton iteration scheme is slightly slower than rate of order 2 in the Newton iteration scheme, the former is more stable and less sensitive to the initial guess. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source]

Continuation of travelling-wave solutions of the Navier,Stokes equations

Isabel Mercader
Abstract 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]