For non-M-matrices, this paper proposes an unstructured multigrid method that only attempts to interpolate in the directions of geometrical smoothness. These directions are determined by analyzing samples of algebraically smooth error, e. Neighboring 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.
This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.