Multilevel Fictitious Space Preconditioner for Nonconforming Approximations on Unstructured Regular Triangulations

Serguei Maliassov

Institute for Mathematics and Its Applications
University of Minnesota
514 Vincent Hall
206 Church Street S.E.
Minneapolis, MN 55455


Abstract

The paper describes an application of a fictitious space technique to constructing a preconditioner for stiffness matrices generated by nonconforming finite element method on unstructured regular triangulations. Given an unstructured mesh, a structured hierarchical mesh is constructed "approximating" in certain sense the original one. Introducing special interpolation operators we reduce the problem of constructing a preconditioner in a space associated with unstructured grid to the problem of constructing one in a fictitious space corresponding to the structured grid. Within the fictitious space we apply multilevel preconditioner with local refinement.