Aggregation-Based Domain Decomposition Methods for Unsaturated Flow II: Theory and Convergence

Lea Jenkins and Tim Kelley

Department of Mathematics Box 8205 North Carolina State University Raleigh, NC 27695


Abstract

Multilevel Schwarz methods are effective preconditioners for elliptic problems. However, developing the restriction and interpolation operators between levels is nontrivial, especially on an unstructured mesh. We have used aggregation ideas from the algebraic multigrid literature to develop our coarse mesh, and we have applied these ideas to problems discretized on 3-d, unstructured meshes. In this talk I will present theoretical results for the bound on the condition number for the preconditioned system using a two-level additive Schwarz preconditioner with aggregation elements for the second level, and give numerical results for our work.