Interface preserving coarsening multigrid for elliptic problems with highly discontinuous coefficients

Abstract

We propose an interface preserving coarsening, a geometric technique for solving discontinuous coefficient partial differential equations by multigrid. It selects coarse grid points so that all the coarse grids are aligned with the interfaces for regular interface problems on structured grids, and so that the interfaces are resolved as much as possible for irregular interface problems. As a result, multigrid with linear interpolation is sufficient to obtain fast convergence. We show by one-dimensional and two-dimensional interface problems that the convergence rate of the resulting multigrid method is independent of the mesh size and the size of the jump at the interfaces. Copyright © 2000 John Wiley & Sons, Ltd.