This paper deals with the numerical solution of a two-dimensional (2-D) magnetostatic field problem. Thereby, a finite element method (FEM) with the magnetic vector potential as field variable and a discretization with edge elements is used. For the efficient solution of the obtained matrix equation system, a geometric multigrid solver (MG) is presented which reduces the number of iterations considerably.
A new preconditioned conjugate gradient (PCG)-based domain decomposition method is given for the solution of linear equations
arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed method is in the
recommended preconditioner which is constructed by using cyclic matrix. The resulting preconditioned algorithms are well suited
to parallel computation.
Authors:Oumnia Elmrabet, Hasnae Boubel, Mohamed Rougui, and Ouadia Mouhat
In the context of verification of civil engineering structures stability and determination of sliding surface and safety factor, a careful analysis of several parameters was carried out to guarantee their safety against failure. To quantitatively forecast failure scope, the embankment dam located on Oued Rhiss in the province of Hocemia is chosen as the model of this study. A static stability analysis is performed by using the Slope/W software. A parametric study performed to evaluate the influence of dam's height, the height of water in the reservoir and the length of drains on the safety coefficient and pore pressures. Reliability analysis elaborated by using the Comrel application, and it allows to statistically quantifying the probability of failure by employing the Monte Carlo distribution. Results show that the dam structure has some weak zones and not strong enough as the safety factor is less than one, it is related to structure's parameters and the drainage system.
Authors:Monika Nagyová, Martin Psotný, and Ján Ravinger
An actual problem of fabrication of pre-stressed concrete prefabricated elements is presented in this article. The steel form could be more than 100 m long. Inserting the polystyrene plates ten or more prefabricates can be produced in one step. The horizontal deformations represent a special problem. The simplification of the elastic support as the friction effect is introduced. The non-linear solution has been used.
The minimum degree ordering is one of the most widely used algorithms to preorder a symmetric sparse matrix prior to numerical factorization. There are number of variants which try to reduce the computational complexity of the original algorithm while maintaining a reasonable ordering quality. An in-house finite element solver is used to test several minimum degree algorithms to find the most suitable configuration for the use in the Finite Element Method. The results obtained and their assessments are presented along with the minimum degree ordering algorithms overview.
A geometric multigrid method for the efficient solution of time-harmonic 3-D eddy-current problems is presented. A finite element method with a scalar potential and a vector potential is used to describe the problem. Numerical examples show that using the right smoother in the multigrid, a good convergence of solutions, which does not deteriorate for bad quality meshes can be obtained. The computation time for solving the eddy-current problem of the multigrid method is much faster than that of the conjugate gradient method with incomplete Cholesky factorization as preconditioner.
Authors:J. El Bahaoui, L. El Bakkali, and A. Khamlichi
Buckling analysis of axially compressed cylindrical shells having one or two localized initial geometric imperfections was performed by using the finite element method. The imperfections of entering triangular form were assumed to be positioned symmetrically at the mid shell length. The buckling load was assessed in terms of shell aspect ratios, imperfection amplitude and wavelength, and the distance separating the imperfections. The obtained results have shown that amplitude and wavelength have major effects, particularly for short and thin shells. Two interacting imperfections were found to be more severe than a single imperfection, but the distance separating them has small influence.
A preconditioned conjugate gradient (PCG)-based domain decomposition method was given in  and  for the solution of linear equations arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed algorithm was that the recommended preconditioner was constructed by using symmetric-cyclic matrix. But we could give only the definitions of the entries of this cyclic matrix. Here we give a short description of this algorithm, the method of calculation of matrix entries and the results of calculation. The numerical experiments presented show, that this construction of precondition in the practice works well.