MULTILEVEL SOLUTION OF CELL VERTEX CAUCHY-RIEMANN EQUATIONS

In this paper a multilevel algorithm for the solution of the cell vert ex finite volume Cauchy-Riemann equations is developed. These equation s provide a linear algebraic system obtained by the finite volume cell vertex discretization of the inhomogeneous Cauchy-Riemann equations. Both square and triangular cells are employed. The system of linear eq uations resulting from the cell vertex discretization is overdetermine d and its solution is considered in the least squares sense. By this a pproach a consistent algebraic problem is obtained which differs from the original one by O(h(2)) perturbation of the right-hand side. A sui table cell-based convergent smoothing iteration is presented which is naturally linked to the least squares formulation. Hence a standard mu ltilevel scheme is presented and discussed which combines the given sm oother and a cell-based transfer operator of the residuals and a node- based prolongation operator of the unknown variables. Some remarkable reduction properties of these operators are shown. A full multilevel a lgorithm is constructed which solves the discrete problem to the level of truncation error by employing one multilevel cycle at each current level of discretization.