Department of Mathematics

Texas A&M University

College Station, TX 77843-3368

and Panayot S. Vassilevski

Center for Applied Scientific Computing

UC Lawrence Livermore National Laboratory

P. O. Box 808, L-560

Livermore, CA 94551

Abstract

Finite element problems posed on large unstructured grids arise naturally in simulations, where only a very fine discretization of the domain is available. In order to achieve performance comparable with multilevel methods for the geometrically refined case, one can use an algebraic solver based on sequence of coarsened meshes.

In this talk we present a possible parallelization of one such algorithm - the agglomeration based algebraic multigrid for finite element problems (AMGe). The method starts with a partitioning of the original domain into subdomains with a generally unstructured finite element mesh on each subdomain. The agglomeration based AMGe is then applied independently in each subdomain. It needs access to the local stiffness matrices which are (variationally) constructed after coarsening. Note that even if one starts with a conforming fine grid, independent coarsening generally leads to non-matching grids on the coarser levels. We use an element-based dual basis mortar finite element method in order to set up global problems on each level. Since the considered AMGe produces abstract elements and faces defined as lists of nodes, the mortar multiplier spaces are also constructed in a purely algebraic way. This construction requires inversion of the local mass matrices on each interface boundary shared between two subdomains, which is possible because of the way AMGe agglomerates the faces. Finally, a multigrid-preconditioned solver is applied to the resulting sequence of (non-nested) spaces. The talk will conclude with set of numerical results illustrating the computational behavior of this new algebraic multigrid algorithm.

This work was performed under the auspices of the U.S. Department of Energy
by the University of California, Lawrence Livermore National Laboratory
under contract No. W-7405-Eng-48.