265 IGPM265.pdf        March 2006
TITLE Multilevel Preconditioning for Partition of Unity Methods - Some Analytic Concepts
AUTHORS Wolfgang Dahmen, Shai Dekel, Pencho Petrushev
ABSTRACT This paper is concerned with the construction and analysis of multilevel Schwarz preconditioners for partition of unity methods applied to elliptic problems. We show under which conditions on a given multilevel partition of unity hierarchy (MPUM) one even obtains uniformly bounded condition numbers and how to realize such requirements. The main anlytical tools are certain norm equivalences based on two-level splits providing frames that are stable under taking subsets.
KEYWORDS Multilevel partition of unity methods, two-level splits, multilevel expansions, additive Schwarz preconditioner, smoothness spaces, local linear independence, stability, Besov spaces
DOI 10.1007/s00211-007-0089-7
PUBLICATION Numerische Mathematik
107(3), 503-532 (2007)