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.