Grid Transfer Operators Research Articles

A multigrid approach for the solution of the 2D semiconductor equations

In this paper a multigrid method for the solution of the steady semiconductor equations is presented. The discretization is made on an adaptive grid, by means of a mixed finite element method on rectangles, with the trapezoidal quadrature rule. In this way the resulting scheme reduces to the well-known Scharfetter-Gummel discretization. The grid transfer operators are selected in accordance with the discretization. The multigrid solution method is based on a collective, symmetric five-point Vanka relaxation, and—in order to admit very coarse grids—a local damping of the coarse grid correction is applied. It is shown that the convergence rate is independent of the grid size. Since nested iteration is combined with the multigrid iteration, the resulting solution method has optimal efficiency.

Analysis of a multigrid strokes solver

Model-problem analysis or local-mode analysis is used to investigate the two-level convergence rates for multigrid Strokes solvers. The solvers are based on the discretization on the staggered grid and the distributive relaxation of the continuity equation. The influence of the grid geometry is analyzed by also considering the Poisson equation on the semistaggered grid. Various grid transfer operators are compared. For an isotropic ( h x = h y discretization, simple tranfer operators are sufficient to obtain optimal rates, but not in the anisotropic case. The theoretical results are compared with observed multigrid convergence rates.