Computational Issues in the Application of Nonlinear Multigrid to Nonlinear Diffusion Problems

Jim Jones

Panayot Vassilevski

Carol S. Woodward

Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Box 808, L-561 Livermore, CA 94551


Our discussion concerns the application of nonlinear multigrid, or FAS, to nonlinear diffusion problems with the eventual target application of variably saturated flow. We will focus on computational issues related to calculation of efficient interpolation and restriction operators for the multigrid V-cycle, as well as appropriate nonlinear coarse grid operators. Our numerical results compare this nonlinear multigrid method with traditional Newton techniques. This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under Contract W-7405-Eng-48