Search results for "Gradient method"
showing 10 items of 38 documents
Optimal measurement setup for damage detection in piezoelectric plates
2009
[EN] An optimization of the excitation-measurement configuration is proposed for the characterization of damage in PZT-4 piezoelectric plates, from a numerical point of view. To perform such an optimization, a numerical method to determine the location and extent of defects in piezoelectric plates is developed by combining the solution of an identification inverse problem, using genetic algorithms and gradient-based methods to minimize a cost functional, and using an optimized finite element code and meshing algorithm. In addition, a semianalytical estimate of the probability of detection is developed and validated, which provides a flexible criterion to optimize the experimental design. Th…
Direct Numerical Methods for Optimal Control Problems
2003
Development of interior point methods for linear and quadratic programming problems occurred during the 1990’s. Because of their simplicity and their convergence properties, interior point methods are attractive solvers for such problems. Moreover, extensions have been made to more general convex programming problems.
A variational inequality approach to constrained control problems for parabolic equations
1988
A distributed optimal control problem for parabolic systems with constraints in state is considered. The problem is transformed to control problem without constraints but for systems governed by parabolic variational inequalities. The new formulation presented enables the efficient use of a standard gradient method for numerically solving the problem in question. Comparison with a standard penalty method as well as numerical examples are given.
A purification algorithm for semi-infinite programming
1992
Abstract In this paper we present a purification algorithm for semi-infinite linear programming. Starting with a feasible point, the algorithm either finds an improved extreme point or concludes with the unboundedness of the problem. The method is based on the solution of a sequence of linear programming problems. The study of some recession conditions has allowed us to establish a weak assumption for the finite convergence of this algorithm. Numerical results illustrating the method are given.
Least-Norm Regularization For Weak Two-Level Optimization Problems
1992
In this paper, we consider a regularization for weak two-level optimization problems by adaptation of the method presented by Solohovic (1970). Existence and approximation results are given in the case in which the constraints to the lower level problems are described by a multifunction. Convergence results for the least-norm regularization under perturbations are also presented.
Gradient-based shape optimisation of ultra-wideband antennas parameterised using splines
2010
Methodology enabling the gradient-based optimisation of antennas parameterised using B-splines is presented. Use of the spline parametrisation allows us to obtain versatile new shapes, whereas the geometry can be represented with a small set of design variables. Moreover, good control over admissible geometries is retained. Advantages of gradient-based optimisation methods are quick convergence, and the fact that the obtained design can be guaranteed to be a local optimum. Focus of this study is to present techniques that enable the computation of exact gradients of the discrete problem, even though the complexity of the geometries does not permit establishing analytical expressions for the…
Some observations on the regularizing field for gradient damage models
2000
Gradient enhanced material models can potentially preserve well-posedness of incremental boundary value problems also after the onset of strain softening. Gradient dependent constitutive relations are rooted in the assumption that some scalar or tensor field, which appears in the yield function, has to be enriched by adding a term involving its second-order gradient field. For gradient-dependent plasticity this term is universally accepted to be the equivalent plastic strain. For gradient-dependent damage models different choices have been presented in the literature. They all possess the desired regularization of the solution, but they are not identical as regards the structural response. …
Controllability method for the Helmholtz equation with higher-order discretizations
2007
We consider a controllability technique for the numerical solution of the Helmholtz equation. The original time-harmonic equation is represented as an exact controllability problem for the time-dependent wave equation. This problem is then formulated as a least-squares optimization problem, which is solved by the conjugate gradient method. Such an approach was first suggested and developed in the 1990s by French researchers and we introduce some improvements to its practical realization. We use higher-order spectral elements for spatial discretization, which leads to high accuracy and lumped mass matrices. Higher-order approximation reduces the pollution effect associated with finite elemen…
Process parameters calibration in 3D tube hydroforming processes
2007
In tube hydroforming the concurrent actions of pressurized fluid and mechanical feeding allow to obtain tube shapes characterized by complex geometries such as different diameters sections and/or bulged zones. What is crucial in such processes is the proper design of operative parameters aimed to avoid defects (for instance shape defects or ductile fractures). The main process parameters are material feeding history (i.e. the punches velocity history) and internal pressure path during the process. In more complex three dimensional processes, also the action of a counterpunch is generally useful to reduce thinning in particular in expansion zones of the tube (i.e. T or Y shaped tubes). The g…
A Numerical Method for an Inverse Problem Arising in Two-Phase Fluid Flow Transport Through a Homogeneous Porous Medium
2019
In this paper we study the inverse problem arising in the model describing the transport of two-phase flow in porous media. We consider some physical assumptions so that the mathematical model (direct problem) is an initial boundary value problem for a parabolic degenerate equation. In the inverse problem we want to determine the coefficients (flux and diffusion functions) of the equation from a set of experimental data for the recovery response. We formulate the inverse problem as a minimization of a suitable cost function and we derive its numerical gradient by means of the sensitivity equation method. We start with the discrete formulation and, assuming that the direct problem is discret…