April 20, 9:30 am
in room MTH 3206, University of Maryland,
College Park
Domain Decomposition Algorithms for Spectral Elements
in Three Dimensions
Prof. Luca Pavarino
Department of Mathematics
University of Pavia
Pavia, Italy
pavarino@cs.umd.edu
Domain decomposition methods have developed rapidly during the last decade,
primarily for lower order finite element methods. These methods provide
preconditioners, for conjugate gradient type methods, for the often very
large and ill-conditioned algebraic systems that arise in finite element
applications. In this talk, we will study some recent efforts to extend
these methods and their analysis to higher order elements. These problems
pose special challenges since their stiffness matrices tend to be even more
ill-conditioned than those of lower order methods. New technical tools are
also required for the analysis. We will consider iterative substructuring
methods based on both Galerkin formulation and Gauss-Lobatto-Legendre
quadrature. For this family of new preconditioners it has been established
that the rate of convergence of the iterative methods is independent of the
number of elements and depends only polylogarithmically on p, the degree of
the elements. Additional preconditioners, including some based on overlapping
Schwarz methods, will also be considered.
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