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.
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.