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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.