Search results for "Finite element method"
showing 10 items of 746 documents
Discretization estimates for an elliptic control problem
1998
An optimal control problem governed by an elliptic equation written in variational form in an abstract functional framework is considered. The control is subject to restrictions. The optimality conditions are established and the Ritz-Galerkin discretization is introduced. If the error estimate corresponding to the elliptic equation is given as a function like where h is the discretization parameter and is an integer, then the error estimates for the optimal control, for the optimal state and for the optimal value are obtained. These results are applied first for a Two-Point BVP and next for a 2D/3D elliptic problem as state equation. Next a spectral method is used in the discretization proc…
A linearization technique and error estimates for distributed parameter identification in quasilinear problems
1996
The identification problem of a nonlinear functional coefficient in elliptic and parabolic quasilinear equations is considered. A distributed observation of the solution of the corresponding equation is assumed to be known a priori. An identification method is introduced, which needs only a linear equation to be solved in each iteration step of the optimization. Estimates of the rate of convergence for the proposed approach are proved, when the equation is discretized with the finite element method with respect to space variables. Some numerical results are given.
A General Investigation on the Differential Leakage Factor for Symmetrical and Asymmetrical Multiphase Winding Design
2020
This work provides an investigation based on a fast estimation of the degree of unbalance (D.U.%) and the differential leakage factor (&sigma
Numerical approach to the exact controllability of hyperbolic systems
2005
In this paper we present the numerical implementation of H.U.M. (Hilbert Uniqueness Method, J.L.Lions[1]). We restrict ourselves to the exact boundary controllability of the wave equation, with Dirichlet controls, but the numerical method presented here can be applied to other kinds of controllability. The problem is discretized by a finite elements of first order in space and by a discrete time Galerkin approximation (Dupont [1]). The efficiency of the method is illustrated by numerical results.
Time-harmonic solution for acousto-elastic interaction with controllability and spectral elements
2010
The classical way of solving the time-harmonic linear acousto-elastic wave problem is to discretize the equations with finite elements or finite differences. This approach leads to large-scale indefinite complex-valued linear systems. For these kinds of systems, it is difficult to construct efficient iterative solution methods. That is why we use an alternative approach and solve the time-harmonic problem by controlling the solution of the corresponding time dependent wave equation. In this paper, we use an unsymmetric formulation, where fluid-structure interaction is modeled as a coupling between pressure and displacement. The coupled problem is discretized in space domain with spectral el…
Time-dependent simulation of Czochralski silicon crystal growth
1997
We have developed a detailed mathematical model and numerical simulation tools based on the streamline upwind/Petrov-Galerkin (SUPG) finite element formulation for the Czochralski silicon crystal growth. In this paper we consider the mathematical modeling and numerical simulation of the time-dependent melt flow and temperature field in a rotationally symmetric crystal growth environment. Heat inside the Czochralski furnace is transferred by conduction, convection and radiation, Radiating surfaces are assumed to be opaque, diffuse and gray. Hence the radiative heat exchange can be modeled with a non-local boundary condition on the radiating part of the surface. The position of the crystal-me…
On the impact of the heat transfer modelling approach on the prediction of EU-DEMO WCLL breeding blanket thermal performances
2020
Abstract The Water-Cooled Lithium-Lead Breeding Blanket is a key component of a fusion power plant, in charge of ensure Tritium production, shield Vacuum Vessel and magnets and remove the heat power deposited by radiation and particles arising from plasma. The last function is fulfilled by First Wall and Breeding Zone independent cooling systems. Several layouts of BZ coolant system have been investigated in the last years to identify a configuration that might guarantee EUROFER temperature below the limit (550 °C) and good thermal-hydraulic performances (i.e. water outlet temperature of 328 °C). A research activity is conducted to study and compare different modelling approaches to simulat…
The simulation of morphology of dissimilar copper–steel electron beam welds using level set method
2010
Abstract In present work, the simulation of morphology and velocity field in dissimilar electron beam welds formed between the metals with limited solubility is described by the example of copper–stainless steel couple. Finite element software COMSOL Multiphysics 3.5 has been employed due to its flexibility in solving of coupled multiphysical problems. The domination of horizontal flows allows reducing the model to two dimensions. Level set method has been used to determine the position of the interface between immiscible components basing on coupled heat transfer and fluid flow pseudo-stationary solution. The evolution of the shape, fluid flow and mixing pattern in function of operational …
The study and optimization of the behavior and energy absorbed in the frontal impact by a rectangular metal workpiece with an Origami core
2021
The bumper systems (beams and face bars) are parts of the car body structure, one of the most important components of an auto vehicle because of its role in absorbing the energy of an impact by deformation. The main objective of this paper is to study, optimize the built shape of the frontal members beams used in the endurance structure of motor vehicles in terms of their ability to absorb internal energy resulting from a frontal impact under the principles of sustainability. The study combines the classical technology used in the construction of vehicles with, the Origami Engineering” technique, which is generally used by NASA, but also by engineers in other fields: aeronautics, nanotechno…
Refined equivalent single layer formulations and finite elements for smart laminates free vibrations
2014
A family of 2D refined equivalent single layer models for multilayered and functionally graded smart magneto-electro-elastic plates is presented. They are based on variable kinematics and quasi-static behavior for the electromagnetic fields. First, the electromagnetic state of the plate is determined by solving the strong form of the electromagnetic governing equations coupled with the corresponding interface continuity conditions and external boundary conditions. The electromagnetic state is then condensed into the plate kinematics, whose governing equations can be written using the generalized principle of virtual displacements. The procedure identifies an effective elastic plate kinemati…