A COMPOSITE NODAL FINITE-ELEMENT FOR HEXAGONS

A nodal algorithm for the solution of the multigroup diffusion equatio ns in hexagonal arrays is analyzed. Basically, the method consists of dividing each hexagon into four quarters and mapping the hexagon quart ers onto squares. The resulting boundary value problem on a quadrangul ar domain is solved in primal weak formulation. Nodal finite element m ethods like the Raviart-Thomas RTk schemes provide accurate analytical expansions of the solution in the hexagons. Transverse integration ca nnot be performed on the equations in the quadrangular domain as simpl y as it is usually done on squares because these equations have essent ially variable coefficients. However, by considering an auxiliary prob lem with constant coefficients (on the same quadrangular domain) and b y using a ''preconditioning'' approach, transverse integration can be performed as for rectangular geometry. A description of the algorithm is given for a one-group diffusion equation. Numerical results are pre sented for a simple model problem with a known analytical solution and for k(eff) evaluations of some benchmark problems proposed in the lit erature. For the analytical problem, the results indicate that the the oretical convergence orders of RTk schemes (k = 0,1) are obtained, yie lding accurate solutions at the expense of a few preconditioning itera tions.