Multilevel Elliptic Solvers on Unstructured Grids

Prof. Tony Chan

Department of Mathematics, University of California at Los Angeles

Unstructured grids have become increasingly popular in scientific computing, primarily due to their flexibility in adapting to complicated geometries and rapid changes in the solution. The lack of an inherent coarse grid hierarchy, however, makes the design of multilevel iterative methods, such as multigrid and domain decomposition methods, much more delicate. In this talk, I'll give an overview of some of the approaches that have been proposed in the literature, as well as some theoretical and numerical results obtained by our group at UCLA. The techniques we have used include the re-triangulation of a maximal independent set of the fine grid points, as well as agglomeration of fine grid triangles. Special care is used at Neumann boundaries where the fine and coarse boundaries are non-matching.