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.
In this paper the field distribution of different electrode arrangements and voltage supply systems has been investigated, and a new method has been developed to analyze them. The ozone production of the electrode arrangement has been investigated experimentally with the voltage supply system, and significant differences were found. The aim of this paper is to highlight the reasons for these differences in ozone production in relation to the potential and electric field distribution. For electrode arrangements the characteristics of the electric field, have been calculated by Finite Element Method completed with the Donor-Cell method for the space charge calculation. The index numbers related to the analysis of the field distribution and the ozone production have strong regression, which makes possible the estimation of the ozone production of the different arrangement.