An unstructured multigrid method based on geometric smoothness

For non-M-matrices, this paper proposes an unstructured multigrid method that only attempts to interpolate in the directions of geometric smoothness. These directions are determined by analysing samples of algebraically smooth error, e. Neighbouring grid points i and j are called smoothly coupled if e(i) and e(j) are consistently nearby in value. In addition, these differences may be used to define interpolation weights. These new ideas may be incorporated into the algebraic multigrid method. Test results show that the new method can have much lower grid and operator complexities compared to AMG, leading to lower solve timings. Published in 2003 by John Wiley Sons, Ltd.