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Polish Academy of Sciences
Imen Debbabi, Zohra Sendi, Hédi BelHadjSalah. A comparison between the improved element-free Galerkin method and the element-free Galerkin method for 2D potential and elasticity problems. CAMES 2016 (23) 2/3: 87-107
In this paper, a comparison between the improved element-free Galerkin (IEFG) method, based on the improved moving least square (IMLS) approximation, and the element-free Galerkin (EFG) method, based on the moving least square (MLS) approximation, is presented. The IMLS approximation is obtained when an orthogonal basis function with a weight function is used. The IMLS approximation has a greater computational efficiency than the existing MLS approximation and does not lead to an ill-conditioned system of equations. The comparison is made for two-dimensional (2D) potential problems and 2D elastic problems. From these problems, the efficiency of the IEFG method is validated by comparing the results obtained with the IEFG method and EFG method with those obtained analytically.
Keywords: EFG method, potential problems, elasticity problems, IMLS approximation.
This paper focuses on the discontinuous Galerkin (DG) method in which the compatibility condition on the mesh skeleton and Dirichlet boundary condition on the outer boundary are enforced with the help of one-dimensional finite difference (FD) rules, while in the standard approach those conditions are satisfied by the penalty constraints. The FD rules can be of arbitrary degree and in this paper the rules are applied up to fourth degree. It is shown that the method presented in this paper gives better results in comparison
to the standard version of the DG method. The method is based on discontinuous approximation, which means that it can be constructed using arbitrary local basis functions in each finite element. It is quite easy to incorporate some global basis functions in the approximation field and this is also shown in the paper. The paper is illustrated with a couple of two-dimensional examples.
Keywords: discontinuous Galerkin method, finite difference, compatibility condition, approximation basis.
In this paper a comparison of the performance of two ways of discretizing the nonlinear convection-diffusion equation in a one-dimensional (1D) domain is performed. The two approaches can be considered within the class of high-order methods. The first one is the discontinuous Galerkin method, which has been profusely used to solve general transport equations, either coupled as the Navier-Stokes equations, or on their own. On the other hand, the ENATE procedure (Enhanced Numerical Approximation of a Transport
Equation), uses the exact solution to obtain an exact algebraic equation with integral coefficients that link nodal values with a three-point stencil. This paper is the first of thorough assessments of ENATE by comparing it with well-established high-order methods. Several test cases of the steady Burgers' equation with and without source have been chosen for comparison.
Keywords: one-dimensional transport equation, high-order methods.
This paper presents the multi-objective optimization process of a hydraulic damper design based on its interdisciplinary meta-model considering both the properties of a damper and of the testing equipment used for the purpose of design criteria verification, and in particular the tolerance band criterion of damping force characteristics, the criterion of maximum permissible vibration level expressed with the piston rod acceleration and the criterion of fatigue durability for the damper's hydraulic valve system. The meta-model of a damper and a testing bench include the following models: mechanical model, hydraulic model, electro-hydraulic model and valve system fatigue durability model. The multi-objective optimization method provides an optimal solution by means of Pareto frontier. Furthermore, all potential feasible solutions are ranked according to additional customer preferences to select the most suitable ones. The proposed method is intended to be used to determine the best starting point in a new shock absorber design process.
Keywords: multi-objective optimization, model-based design, shock absorber model.